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# Recent problems solved by 'stanbon'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239, >>Next

 Linear-systems/100310: This is my question... Answer the following information about this line: y = 2x-3 m=_______ b=_______ Find the x or y for the following points on the above line: (0,__) , (___, 0) , (1,___0 , (____, 9) I am clueless how to anwser this...HELP!!!!!! 1 solutions Answer 73049 by stanbon(57282)   on 2007-09-25 15:31:39 (Show Source): You can put this solution on YOUR website!Answer the following information about this line: y = 2x-3 m=2______ b=-3_______ Find the x or y for the following points on the above line: (0,-3__) , (3/2___, 0) , (1,-1___) , (6____, 9) ------------------ Cheers, Stan H.
 test/100255: From the information in the table providing values of f(x) and g(x), evaluate (f o g)^-1 (2) x 1 2 3 4 5 f(x) 3 4 5 1 2 g(x) 5 4 2 3 11 solutions Answer 73048 by stanbon(57282)   on 2007-09-25 15:29:10 (Show Source): You can put this solution on YOUR website!From the information in the table providing values of f(x) and g(x), evaluate (f o g)^-1 (2) x 1 2 3 4 5 f(x) 3 4 5 1 2 g(x) 5 4 2 3 1 ----------------- (fog)^-1(x) = (g^-1of^-1)(x) Your Problem = g^-1[f^-1(2)] = g^-1[5] = 1 ============= Cheers, Stan H.
 Systems-of-equations/100303: Please help me solve this equation - It is in fractions- I keep getting lost in my work 5+ x/3 = 2x/5 -7 X= at one point I had it set up and worked as 75 + 15x/5 = 30x/15 - 105 75x = 2X -105 If I am on the right path I am lost on what to do next- If I am completely wrong then I need help from the beginning. Please advise1 solutions Answer 73047 by stanbon(57282)   on 2007-09-25 15:24:36 (Show Source): You can put this solution on YOUR website!5+ x/3 = 2x/5 -7 ------------------- x/3 - 2x/5 = -12 Multiply thru by 15 to get: 5x - 3*2x = -12*15 -x = -12*15 x = 150+30 = 180 ================= Cheers, Stan H. Cheers, Stan H.
 Equations/100308: In Ajax Corporation, the first shift produced 4 1/2 times as many lightbulbs as the second shift. If the number of lightbulbs was 55,000 how many lightbulbs were produced on each shift? Solve the unknown 1 solutions Answer 73046 by stanbon(57282)   on 2007-09-25 15:20:30 (Show Source): You can put this solution on YOUR website!In Ajax Corporation, the first shift produced 4 1/2 times as many lightbulbs as the second shift. If the number of lightbulbs was 55,000 how many lightbulbs were produced on each shift? ----------- Let # produced by 2nd shift be "x". Then # produced by 1st shift = 4.5 x ------------- EQUATION: x + 4.5x = 55000 5.5x = 55000 x = 10,000 (# produced by 2nd shift) 4.5x = 45000 (# produced by 1st shift) =============== Cheers, Stan H.
 Equations/100266: This question is from textbook College Algebra and Trigonometry A sewage treatment plant has two inlet pipes to its settling pond. One can fill the pond in 10 hr, the other in 12 hr. If the first pipe is open for 5 hr and then the second pipe is opened, how long will it take to fill the pond?1 solutions Answer 73045 by stanbon(57282)   on 2007-09-25 15:16:59 (Show Source): You can put this solution on YOUR website!A sewage treatment plant has two inlet pipes to its settling pond. One can fill the pond in 10 hr, the other in 12 hr. If the first pipe is open for 5 hr and then the second pipe is opened, how long will it take to fill the pond? ----------------- 1st pipe DATA: Time to fill = 10 hr/job ; Rate = 1/10 job/hr ----------------- 2nd pipe DATA: Time to fill = 12 hr/job ; Rate = 1/12 job/hr ---------------- EQUATION:(since half of the pond has already been filled) Let x = time for the two pipe together to fill half the pond x(1/10 + 1/12) = 1/2 x(22/120)= 1/2 x(11/60) = 1/2 x(11/30) = 1 x = 30/11 = 2 hrs (8/11) hr (8/11)*60 = 43.6 minutes Total time for the two pipes to fill half the pond = 2 hrs 43.6 minutes =================== Cheers, Stan H.
 Polynomials-and-rational-expressions/100286: factor completely 3xsquared-8x-31 solutions Answer 73044 by stanbon(57282)   on 2007-09-25 15:02:52 (Show Source): You can put this solution on YOUR website!factor completely 3xsquared-8x-3 3x^2-8x-3 = 3x^2-9x+x-3 =3x(x-3)+(x-3) =(x-3)(3x+1) =============== This is called the AC method of factoring ================ Cheers, Stan H.
 Linear-equations/100284: x y 3 56 4 42 growth rate ? percent decrease ? My professor told me to use slope formula but I do not know what they are asking.1 solutions Answer 73042 by stanbon(57282)   on 2007-09-25 14:53:28 (Show Source): You can put this solution on YOUR website!x y 3 56 4 42 growth rate ? percent decrease ? ------------------ growth rate is the slope from (3,56) to (4,42) slope = [42-56]/[4-3]= -14 -------------------- percent decrease is -14*100/100 = -1400 % ================ Cheers, Stan H.
 Rational-functions/100256: Hello, I am having a hard time finding domains. For example: f(x) = 1/x-2? This makes no sense to me. Please help.1 solutions Answer 73005 by stanbon(57282)   on 2007-09-25 09:01:47 (Show Source): You can put this solution on YOUR website!x cannot be "2"because x=2 would make the denominator zero which would make f(x) meaningless. Therefore the Domain is "all Real Numbers except x=2". Cheers, Stan H.
 Expressions-with-variables/100201: This question is from textbook Algebra structure and Method Please help me confirm I am doing this correctly: 4(2(-5x+y)-y)-10(y-4X) with the outside set of parenthesis being brackets1 solutions Answer 72980 by stanbon(57282)   on 2007-09-24 22:57:43 (Show Source): You can put this solution on YOUR website!4(2(-5x+y)-y)-10(y-4X) = 4(-10x+2y-y)-10y+40x = 4(-10x+y)-10y+40x = -40x+4y-10y+40x = -6y ======================== Cheers, Stan H.
 Square-cubic-other-roots/100210: -4 sq root3 - sq root36 + 3 sq root 48 =?1 solutions Answer 72978 by stanbon(57282)   on 2007-09-24 22:49:14 (Show Source): You can put this solution on YOUR website!-4 sq root3 - sq root36 + 3 sq root 48 =? = -4sqrt(3) - 6 + 3sqrt(16)*sqrt3 = -4sqrt(3) -6 +3*4sqrt(3) = -4sqrt(3) - 6 + 12sqrt(3) = 8sqrt(3) - 6 ==================== Cheers, Stan H.
 Square-cubic-other-roots/100209: Tutor I was wondering if you could help me with these two problems? 1.) Sqrt of 50 (use property 1 to simplify each radical expression. Assume all variables represent positive real numbers.) I got 5 sqrt of 10 is this correct? 2.) sqrt of 72x^3 is the answer 3x sqrt of x? Thank you for helping me with these problems I appreciate the help. 1 solutions Answer 72976 by stanbon(57282)   on 2007-09-24 22:42:12 (Show Source): You can put this solution on YOUR website!1.) Sqrt of 50 (use property 1 to simplify each radical expression. Assume all variables represent positive real numbers.) I got 5 sqrt of 10 is this correct? sqrt(50) = sqrt(25)*sqrt(2) = 5sqrt(2) ===================== 2.) sqrt of 72x^3 is the answer 3x sqrt of x? sqrt(72x^3) = sqrt(36x^2)*sqrt(2x)= 6xsqrt(2x) ================== Cheers, Stan H.
 Graphs/100206: This question is from textbook Intermediate Algebra through Applications I just took a quiz online and I knew everything, but for some reason this question stumped me. I looked in the chapter to find a problem like this and there were none. How do you solve this: (4,-3) (3,b) m= -4/5 find b the answer was something like -34/5 ???????? Thanks a lot!!! 1 solutions Answer 72971 by stanbon(57282)   on 2007-09-24 22:18:45 (Show Source): You can put this solution on YOUR website!(4,-3) (3,b) m= -4/5 find b ----------------- slope = change in y / change in x slope = [b--3]/[3-4] = [b+3]/[-1] Since m= -4/5 and since m is the slope you get the following equation: (b+3)/-1 = -4/5 b+3 = 4/5 b = -3 + 4/5 b = -15/5 + 4/5 b = -11/5 ============== Cheers, Stan H.
 Expressions-with-variables/100197: This question is from textbook middle grades math Please help show me where i am going wrong; On the two days before a swim meet, jesse swan a total of 2050 meters. The second day she swam 250 meeters more than the first day. How many meters did she swim on each day? m+250=2050 m=1800 1800-250=500 500+250=750 1st day 2050-750=1600 2nd day I know this to be wrong, book says 900 and 11501 solutions Answer 72966 by stanbon(57282)   on 2007-09-24 21:48:46 (Show Source): You can put this solution on YOUR website!On the two days before a swim meet, jesse swan a total of 2050 meters. The second day she swam 250 meeters more than the first day. How many meters did she swim on each day? ---------------- 1st day she swam "x" miles 2nd day she sham "x+250" miles EQUATION: x + x+250 = 2050 2x = 1800 x = 900 (distance she swam on the 1st day) x+250 = 1150 ( distance she swam on the 2nd day) ================ Cheers, Stan H.
 Surface-area/100160: This question is from textbook Pre-algebra Problem: 2 by 5 rectangle find area : 20in (9-24-07) question: When you come up with your answer on an area problem would the answer be squared??? sorry it has completely escaped my mind. request: If you could I kind of need the answer before school tomorrow. 8th grade Pre-algebra1 solutions Answer 72939 by stanbon(57282)   on 2007-09-24 19:30:10 (Show Source): You can put this solution on YOUR website!Yes, an area answer is always square inches, square feet, or square something. Cheers, Stan H.
 Systems-of-equations/100150: explain why y= 1*1 is not linear1 solutions Answer 72935 by stanbon(57282)   on 2007-09-24 19:15:17 (Show Source): You can put this solution on YOUR website!It is linear. y = 0x + 1 is a linear function. Cheers, Stan H.
 Expressions-with-variables/100149: I'm having real difficulty with the equation: 1 solutions Answer 72931 by stanbon(57282)   on 2007-09-24 18:58:54 (Show Source): You can put this solution on YOUR website!x divided by 3 + y divided by 2 =3 --------------- x/3 + y/2 = 3 Multiply thru by 6 to get: 2x + 3y = 18 3y = -2x + 18 y = (-2/3)x + 6 ===================== Cheers, Stan H.
 Inequalities/100148: Can someone please help me to simplify this without negative exponents? (xy^5 / x^-4y^2)^-21 solutions Answer 72930 by stanbon(57282)   on 2007-09-24 18:56:30 (Show Source): You can put this solution on YOUR website!(xy^5 / x^-4y^2)^-2 ----------------- Comment: The negative sign means "invert"; the 2 means "square" 1st: Invert to get: (x^-4y^2/xy^5)^2 2nd: Square to get: (x^-8 y^4 / x^2 y^10) 3rd: Simplify: (y^4 / x^10 y^10) ================== Cheers, Stan H.
 Expressions-with-variables/100138: This question is from textbook Glenco Algebra I The Yankee Clipper leaves the pier at 9:00 AM at 8 knots. A half hour later, The River Rover leaves the same pier in the same direction traveling at 10 knots. At what time will The River Rover overtake The Yankee Clipper? I'm not sure how to solve this when both time and distance are missing. Thanks.1 solutions Answer 72926 by stanbon(57282)   on 2007-09-24 18:50:58 (Show Source): You can put this solution on YOUR website!The Yankee Clipper leaves the pier at 9:00 AM at 8 knots. A half hour later, The River Rover leaves the same pier in the same direction traveling at 10 knots. At what time will The River Rover overtake The Yankee Clipper? --------------- Comment: That is what algebra is all about; if something is missing, call it "x" and solve for it. ------------------------- Clipper DATA: Rate = 8 knots ; Distance = x miles ; time = d/r = x/8 hrs. ----------------- Rover DATA: Rate = 10 knots; Distance = x miles ; time = d/r = x/10 hrs. ----------------- EQUATION: Cipper time = Rover time + (1/2) hr. x/8 = x/10 + (1/2) Multiply thru by 40 to get: 5x = 4x + 20 x = 20 miles Clipper time = 20/8= 5/2 hrs. 9:00 plus (5/2) hrs = 11:30 AM Rover will over take Clipper at 11:30 AM ================== Cheers, Stan H.
 Functions/100140: What is the domain of the function: f(x) = 2x + 3 when the range is {5,7,9}? f(x) = 1/4x + 3 when the range is {3, -17, 27}? f(x) = -3x - 5 when the range is {-2, 0, 3}?1 solutions Answer 72923 by stanbon(57282)   on 2007-09-24 18:42:57 (Show Source): You can put this solution on YOUR website!What is the domain of the function: f(x) = 2x + 3 when the range is {5,7,9}? In three separate steps, set f(x) = 5, then 7, then 9 and solve for x: x =1 , 2, 3 Domain: {1,2,3} ------------------------------- f(x) = 1/4x + 3 when the range is {3, -17, 27}? x = 0, -80, 120 Domain: {0,80,120} f(x) = -3x - 5 when the range is {-2, 0, 3}? x = -1, -5/3, -8/3 ---------------------------- Cheers, Stan H.
 Miscellaneous_Word_Problems/100139: A club charters a plane at a cost of \$15840 to take a group of members on a trip. At the last minute, 6 people in the group canceled, increasing the cost per person by \$20. How many people originally intended to take this trip? I set the original # of people = P Cost/person = 15840/P The people that went were = (P-6) Final cost/person = 15840/(P-6)= 15840/P + 20 I did do a methodical 'guess and check' and did get what I think is the right answer (72), but how do I really work it out. On a test, that will be too time consuming and in the real work, it is not practical. Help! Also what would you classify this problem as? Thanks 1 solutions Answer 72920 by stanbon(57282)   on 2007-09-24 18:36:21 (Show Source): You can put this solution on YOUR website!15840/(P-6)= 15840/P + 20 Multiply thru by P(P-6) to get: 15840P = 15840(P-6) + 20P(P-6) 15840P -15840P +15840*6 = 20P^2-120P 20P^2-120P-15840*6 = 0 Divide thru by 20 to get: P^2 - 6P -792*6 = 0 (P - 72)(P + 66) = 0 Positive answer: P = 72 ================= Cheers, Stan H.
 Money_Word_Problems/100096: An aid in the mathematical department office gets paid \$3 per hour for clerical work and \$8 per hour for tutoring. If she wants to work a total of 20 hours and earn at least \$145, what is the maximum number of hours X she can spend on clerical work?1 solutions Answer 72882 by stanbon(57282)   on 2007-09-24 16:16:55 (Show Source): You can put this solution on YOUR website!An aid in the mathematical department office gets paid \$3 per hour for clerical work and \$8 per hour for tutoring. If she wants to work a total of 20 hours and earn at least \$145, what is the maximum number of hours X she can spend on clerical work? ------------------ Let number of hours of clerical work be "x" ; pay for this is 3x dollars Number of hours of tutoring is "20-x"; pay for this is 8(20-x)= 160-8x dollars ----------------------- EQUATION: pay + pay =145 dollars 3x + 160-8x = 145 -5x = -15 x = 3 (number of clerical hours) 20-x = 17 (number of tutoring hours) ================ Cheers, Stan H.
 Numbers_Word_Problems/100098: This question is from textbook Sullivan College Algebra A builder of tract homes reduced the price of a model by 15%. If the new price is \$425,000, what was it's original price? How much can be saved by purchasing thr model?1 solutions Answer 72880 by stanbon(57282)   on 2007-09-24 16:10:33 (Show Source): You can put this solution on YOUR website!A builder of tract homes reduced the price of a model by 15%. If the new price is \$425,000, what was it's original price? How much can be saved by purchasing thr model? ----------------- Let the original price be "x". EQUATION: x - 0.15x = 425,000 0.85x = 425,000 x= \$500,000 Cheers, Stan H.
 real-numbers/100106: Determine if sqrt 77 and sqrt(-)are irrational or rational. I said that 77 was because it could be 77/1, however that would only be 77, so now I have changed my mind. I say sqrt77 is irrational. Sqrt(-)is not a real number, so haw can it be rational, So I say it is also irrational. Am I correct or no? I completely do not understand the irrational and rational problems. I have read all that has been answered on here trying to comprehend the rules of them. This is not a problem out of my book, however I have enclosed the book I have been working from.1 solutions Answer 72879 by stanbon(57282)   on 2007-09-24 16:06:42 (Show Source): You can put this solution on YOUR website!Sqrt(77) is irrational because 77 is not a perfect square. sqrt(-1) is neither rational or irrational; it is imaginary. ------------------- The Real Numbers set is made up of the rational numbers and the Irrational numbers. Rationals are numbers that can be written as a ratio of two integers such as 3, 2/3, 5%, 0.123 etc. Irrationals cannot be written as a ratio of integers such as sqrt2, cube root of 5, pi, 0.12345678.....endlessly ------------ Another way to describe irrational numbers is that they do not have a repeating decimal form. So 0.292929292...is rational but 0.299229992992229999922....is irrational =============== Cheers, Stan H.
 Quadratic_Equations/100109: How can I find the vertex while using the quadratic formula?1 solutions Answer 72877 by stanbon(57282)   on 2007-09-24 15:58:02 (Show Source): You can put this solution on YOUR website!How can I find the vertex while using the quadratic formula? ---------------- The quadratic formula says there are roots at (-b/2a)+sqrt(b^2-4ac)/(2a) and (-b/2a) - sqrt(b^2-4ac)/2a So (-b/2a) is the x-value half-way between the two roots. It is therefore on the axis of symmetry of the parabola. It is therefore the x-value of the vertex of the parabola Therefore the vertex is at (-b/2a, f(-b/2a)) ================ Cheers, Stan H.
 logarithm/100110: Solve LOGa(7x+1)=LOGa(4x+16)1 solutions Answer 72876 by stanbon(57282)   on 2007-09-24 15:52:38 (Show Source): You can put this solution on YOUR website!Solve LOGa(7x+1)=LOGa(4x+16) ------------ Since the logs are the same the anti-logs must be equal: 7x+1 = 4x+16 3x = 15 x = 5 ========== Cheers, stan H.
 Problems-with-consecutive-odd-even-integers/99979: Five times the sum of a number and 3 is the same as 3 multiplied by 1 less than twice the number. What is the number?1 solutions Answer 72875 by stanbon(57282)   on 2007-09-24 15:50:26 (Show Source): You can put this solution on YOUR website!Five times the sum of a number and 3 is the same as 3 multiplied by 1 less than twice the number. What is the number? ------------------------------ Let the number be "x". EQUATION: 5(x+3) = 3(2x-1) 5x+15 = 6x-6 x = 21 ============= Cheers, Stan H.
 Graphs/100001: Hello I have a couple of questions I need you to do for me! Thanks!! 1. Find both the x-intercept and the y-intercept of the line given by the equation 3x+7y-11=0 2. What is the slope of the line ? 4x-3y=-2 3. The cost of water use (in dollars) is a linear function of the amount of water used (in hundreds of cubic feet, HCF), as shown in the figure below. The cost for using 14 HCF of water is \$31.40 , and the cost for using 47 HCF is \$ 82.55 . What is the cost for using 26 HCF of water? 4. Carmen is a software saleswoman. Carmen's monthly salary is plus an additional for every copy of Math is Fun she sells. Let S represent Carmen's monthly salary (in dollars), and let N represent the number of copies of Math is Fun that she sold. Write an equation relating to S to N , and then graph your equation. 1 solutions Answer 72823 by stanbon(57282)   on 2007-09-23 22:02:46 (Show Source): You can put this solution on YOUR website!1. Find both the x-intercept and the y-intercept of the line given by the equation 3x+7y-11=0 --------- x-intercept: let y = 0 and solve for x: x=11/3 y-intercept: let x = 0 and solve for y: y = 11/7 ------------------------------------------------------- 2. What is the slope of the line ? 4x-3y=-2 slope = 4/3 ----------------------------------------- 3. The cost of water use (in dollars) is a linear function of the amount of water used (in hundreds of cubic feet, HCF), as shown in the figure below. The cost for using 14 HCF of water is \$31.40 , and the cost for using 47 HCF is \$ 82.55 . What is the cost for using 26 HCF of water? ------- You have two points: (14,31.40),(47,82.55) slope = [82.55-31.40]/[47-14] = 1.55 Form of the equation: cost = slope(HCF count) + b 31.40 = 1.55*14 + b b = 9.7 ---------- EQUATION: cost = 1.55(HCF count) 9.7 --------------- If HCF count = 26 then: price = 1.55*26+9.7 price = 50 =================== Cheers, Stan H.
 Rational-functions/99987: Hello! The directions for this problem are to find the domain and graph the problem. The problem is {abs(x) + abs(y)<_ 1} It would be read as "The absolute value of x plus the absolute value of y is less than or equal to 1." Any help with solving this problem would be great. Thank you!1 solutions Answer 72818 by stanbon(57282)   on 2007-09-23 21:45:20 (Show Source): You can put this solution on YOUR website!find the domain and graph the problem. The problem is {abs(x) + abs(y)<_ 1} ---------------- To see the answer let x = -2,then -1, then 0, then 1, then 2 The domain is (-1,1) and the range is (-1,1) ======================== Cheers, Stan H.
 Linear_Algebra/99997: Please help me in this problem. I need to find the value of x and y by using substitution or elimination. Thank you {y=x {x-4y=01 solutions Answer 72814 by stanbon(57282)   on 2007-09-23 21:37:48 (Show Source): You can put this solution on YOUR website!y=x {x-4y=0 --------------- Substitute 1st into 2nd to get: x-4x=0 -3x = 0 x = 0 y = 0 ======================== Cheers, Stan H.