Tutors Answer Your Questions about Linearsystems (FREE)
Question 994780: Is point (4,5) part of the solution for 3x – 6y ≤ 30? Why or why not?
Answer by josgarithmetic(13975) (Show Source):
Question 994697: A movie theater charges $ 8 for adults and $ 6 for seniors. On a particular day when 344 people paid an admission, the total receipts were $ 2575. Round your answers to the nearest integers.
Answer by Boreal(1464) (Show Source):
You can put this solution on YOUR website! adults=x
seniors=y
x+y=344
8x+6y=2575
6x6y= 2064, multiplying the top equation by (6)
2x=511
x=255.5 or 256 adults
y=88 seniors
256*$8=$2048
88*$6=$528
$2576
===
Question 994700: An airplane travels 2310 miles in 3.5 hours with the aid of a tail wind. It takes 4 hours for the return trip, flying against the same wind. Find the speed of the airplane in the still wind, and the speed of the wind.
Answer by Alan3354(47455) (Show Source):
You can put this solution on YOUR website! Find the 2 groundspeeds, upwind and downwind.
The plane's airspeed is the average of the 2.

Windspeed = difference between airspeed and groundspeed.
Question 994661:
(1 pt)
Solve the given system, using the substitution method.
y = 3x – 4
9x – 3y = 14
A.
There is no solution.
B.
(12, 14)
C.
(14, 12)
D.
There are an infinite number of solutions.
Answer by stanbon(69061) (Show Source):
You can put this solution on YOUR website! Solve the given system, using the substitution method.
y = 3x – 4
9x – 3y = 14

9x3(3x4) = 14

9x  9x + 12 = 14

12 = 14

That is a contradiction.
Ans: No solution

Cheers,
Stan H.
Question 994607: what is the value of x in the solution of the system?
3xy+2z=7
2y+z=5
3x+6y=21
A.4
B.3
C.2
D.1
Answer by Fombitz(25151) (Show Source):
Question 994564: The ordered pairs in each exercise are for the same direct variation. Find each missing value. (1,y) and (2/3,9)
Your help is greatly appreciated! THANK YOU!
Answer by stanbon(69061) (Show Source):
You can put this solution on YOUR website! The ordered pairs in each exercise are for the same direct variation. Find each missing value. (1,y) and (2/3,9)

y/1 = 9/(2/3)

y = 27/2

y = 13.5

Cheers,
Stan H.

Question 994380: I have been trying to solve the following linear equation
3X5Y=11
2x6y=2
I keep getting the wrong answer so when I checked with you guys I noticed that it was substituted with 2(115y)/36y=2
I understand the substitution part but how do I solve from here what does the / mean next to the 3 what operation I'm suppose to there, I'm confused please help.
Found 2 solutions by rothauserc, Alan3354: Answer by rothauserc(2272) (Show Source):
You can put this solution on YOUR website! 3x 5y = 11
2x 6y = 2
************************
solve second equation for x
add 6y to both sides of =
2x = 6y + 2
divide both sides of = by 2
x = 3y + 1
************************
now substitute for x in first equation
3(3y + 1)  5y = 11
9y + 3  5y = 11
4y + 3 = 11
subtract 3 from both sides of =
4y = 8
divide both sides of = by 4
y = 2
******************************************
substitute for y in first equation
3x  5(2) = 11
3x  10 = 11
add 10 to both sides of =
3x = 21
divide both sides of = by 3
x = 7
*****************************************
solution is x = 7 and y = 2
****************************************
check this solution by substituting the solution in the second equation
2(7) 6(2) = 2
14  12 = 2
2 = 2
our solution checks
Answer by Alan3354(47455) (Show Source):
You can put this solution on YOUR website! I have been trying to solve the following linear equation
3X5Y=11
2x6y=2 divide by 2 > x  3y = 1 > x = 3y + 1

Sub for x in the 1st eqn
3X5Y=11
3(3y+1)  5y = 11
9y+3  5y = 11
4y = 8
y = 2

x = 3y + 1
x = 7
Question 994169: how do I solve 4(y  1) + 5(y + 2) = 3(y – 8)
Answer by MathLover1(11324) (Show Source):
Question 994172: Find four solutions of each equation. Write the solutions as ordered pairs. y=12
Answer by stanbon(69061) (Show Source):
You can put this solution on YOUR website! Find four solutions of each equation. Write the solutions as ordered pairs. y=12

Ans:
(1,12); (2,12); (3,12,); (100,12)

Cheers
Stan H.

Question 994178: Carissa makes bracelets to sell at craft fairs. The supplies she needed to start her business cost her $45. In addition, the supplies for each bracelet cost her $3. She sells her bracelets for $5. What is the minimum number of bracelets she must sell to make a profit?
2. Write an equation that Carissa could use to determine her total cost, 'C', for making 'n' bracelets
3. Write an equation she could use to find the profit, 'P', she makes from selling 'n' bracelets
Answer by solver91311(20879) (Show Source):
Question 994183: Caryssa makes bracelets to sell at craft fairs. The supplies she needed to start her business cost her $45. In addition, the supplies for each bracelet cost her $3. She sells her bracelets for $5. What is the minimum number of bracelets she must sell to make a profit.
2. Write an equation that Caryssa could use to determine her total cost, "C", for making "n" bracelets.
3. Write an equation that she could use to find the profit, "P", she makes from selling "n" bracelets.
Answer by solver91311(20879) (Show Source):
Question 993698: Good morning or afternoon whichever time zone you are in. I have a question about a linear equation I would like to ask. The problem is:
x=74y
6x5y=45
My question is, with the equation x=74y, do I add 4y to both sides of the equation so it looks like x+4y=7, before continuing to solve the rest of the problem?
Answer by Fombitz(25151) (Show Source):
You can put this solution on YOUR website! No, you should substitute for x in the second equation with the first equation.
Then solve for y.
Then go back and use the first equation to solve for x.
Question 993634: determined the quadratic function whose graph is given. the vertex is (3,11) and the yintercept is 2
Answer by MathLover1(11324) (Show Source):
Question 993548: What is the ordered pair for x+y=160 and x=4y+30
Answer by ikleyn(988) (Show Source):
You can put this solution on YOUR website! .
What is the ordered pair for x+y=160 and x=4y+30?

You are lucky! You just have x expressed via y: x=4y+30.
Now substitute it into the first equation. In this way you will exclude x and will obtain a single equation for y only:
(4y+30) + y = 160.
Simplify and solve it:
5y = 130,
y = = 26.
Now substitute the found value of y into the second equation of the original system to get x:
x = 4*26 + 30 = 104 + 30 = 134.
Answer. x = 134, y = 26.
Question 993464: How do i solve. 2/3(k—9)= 4(k—19)
Answer by farohw(153) (Show Source):
Question 993497: What is the slope of 15x+20y=2
Answer by solver91311(20879) (Show Source):
Question 993486: I.M. Rich, distributes his fortune as follows and in this order:
 The first $5 million goes to my best friend, Sam, my dog;
 Half the remainder goes to my high school teacher;
 Then, I give $50 million to build a new hospital in town;
 Of the remaining amount, 50% goes to my wife, 40% to my daughter, 9% to my lawyer, and 1% to my lazy son.
All the son gets is $10,000
How much was I.M. Rich's fortune? Justify your answer
How much did each person receive?
Answer by macston(4006) (Show Source):
You can put this solution on YOUR website! .
Start with the remaining amount at the end:
The son's 1% of the remaining amount was $10,000,
so the remaining amount was $10000/0.01=$1,000,000.
Plus what was given to the hospital is $51,000,000.
This is the other "half the remainder"
The first half went to the teacher, so both halves
were $102,000,000.
Add back the $5,000,000 to Sam, the total fortune was $107,000,000
.
CHECK:
From the beginning:
$107,000,000.....$5,000,000 to Sam leaves
$102,000,000.....$51,000,000 to teacher leaves
_$51,000,000.....$50,000,000 for hospital leaves
.._$1,000,000.....$500,000 wife's 50% leaves
___$500,000.....$400,000 daughter's 40% leaves
___$100,000.....$90,000 lawyer's 9% leaves
..___$10,000.....Lazy son's share=$10,000
Question 993366: the cost of a gym membership includes the initial fee and a monthly fee. Find the initial and monthly fees if the total cost for 5 months is $225 and the total cost for 10 months is $375.
Answer by macston(4006) (Show Source):
You can put this solution on YOUR website! .
M=monthly fee; F=initial fee
.
Total cost=initial fee+(number of months)(monthly fee)
.
$225=F+5M
$2255M=F
.
$375=F+10M
$375=($2255M)+10M
$375=$225+5M
$150=5M
$30=M
ANSWER 1: The monthly fee is $30.
.
$225=F+5M
$225=F+5($30)
$225=F+$150
$75=F
ANSWER 2: The initial fee is $75
.
CHECK:
$375=F+10M
$375=$75+10($30)
$375=$75+$300
$375=$375
Question 992946: What is the slope of 2y+1=0?
Answer by josgarithmetic(13975) (Show Source):
Question 992577: Please help me solve this hw question
Find a slopeintercept form equation for the line Through (3,3) with slope of 2/5
Found 2 solutions by jim_thompson5910, MathLover1: Answer by jim_thompson5910(33401) (Show Source): Answer by MathLover1(11324) (Show Source):
Question 992422: Please help me solve
Answer by solver91311(20879) (Show Source):
You can put this solution on YOUR website!
Distribute 2 across the binomial factor in the LHS. Collect like terms. Add the additive inverse of the constant term in the LHS to both sides of the equation. Multiply both sides of the equation by the reciprocal of the coefficient on the variable.
John
My calculator said it, I believe it, that settles it
Question 992405: x+y=k
xy=k
the solution to the system shown is
(0,k)
(2,2)
(k,0)
Answer by stanbon(69061) (Show Source):
You can put this solution on YOUR website! x+y=k
xy=k

Add and solve for "x":
2x = 2k
x = k

Solve for "y"
k + y =k
y = 0

Solution: (k,0)
Cheers,
Stan H.

the solution to the system shown is
(0,k)
(2,2)
(k,0)
Question 992311: 3X + y = 1
5x + y = 1
Answer by Timnewman(249) (Show Source):
Question 992238: Can you please help me. It is solving linear equations with fraction.
3/2x + 1/5= 3/4
My LCD is 20.
Thank you
Answer by macston(4006) (Show Source):
Question 991842: The diameter of a sphere is reduced by 10%. By what percent will the volume be reduced?
Answer by Theo(5548) (Show Source):
You can put this solution on YOUR website! since diameter = 2 times the radius, then if you reduce the diameter by 10%, you also reduce the radius by 10%.
for example:
assume the diameter is 10.
reduce it by 10% and the diameter is now 9.
since the diameter is 10, the radius has to be 10/2 = 5.
since the reduced diameter is 9, the reduced radius has to be 9/2 = 4.5.
5  4.5 is equal to .5 and .5 / 5 is equal to .10 which is equal to 10%, so the radius has been reduced by 10% as well.
the formula for the volume of a sphere is 4/3 * pi * r^3.
when you reduce the radius by 10%, the resulting radius is 90% of the original radius.
this is because r  .10 * r is equal to r * (1  .10) which is equal to r * .9.
reduce the radius by 10% and the formula becomes v = 4/3 * pi * (.9*r)^3 which becomes v = 4/3 * pi * .9^3 * r^3 which then becomes v = 4/3 * pi * .729 * r^3.
this can be rewritten as v = .729 * 4/3 * pi * r^3.
the volume has been reduced by (1  .729) = .271, or 27.1%.
let's take an example:
assume the diameter of the sphere is 24 inches.
the radius then has to be 12 inches because the length of the radius is half the length of the diameter.
the volume of the sphere is 4/3 * pi * 12^3 which is equal to 4/3 * pi * 1728.
reduce the diameter by 10%.
24  .10 * 24 = 24  2.4 = 21.6
this is the same as .9 * 24 which is equal to 21.6.
this is because 24  .10 * 24 is equal to 24 * (1  .10) which is equal to .9 * 24.
the radius of this sphere is equal to 21.6 / 2 = 10.8
the volume of this sphere is equal to 4/3 * pi * (10.8)^3 which is equal to 4/3 * pi * 1259.712.
the volume of the original sphere is 4/3 * pi * 1728.
the volume of the reduce sphere is 4/3 * pi * 1259.712.
the difference in the volume is 4/3 * pi * 1728  4/3 * pi * 1259.712.
this can be rewritten as 4/3 * pi * (1728  1259.712) which can then be simplified to 4/3 * pi * 468.288.
the ratio of this difference to the original volume is:
(4/3 * pi * 468.288) / (4/3 * pi * 1728).
4/3 * pi / 4/3 * pi cancels out because it is equal to 1 and you are left with:
the ratio of the difference is equal to 468.288 / 1728 which is equal to .271 which is equal to 27.1%.
reduce the diameter of the sphere by 10% and you reduce the volume of the sphere by 27.1%.
Question 991747: Is 55y=8x+25 a equation?
Answer by Alan3354(47455) (Show Source):
Question 991488: The Community College basketball team made 51 field goals in a game, some were 2 pointers, and some were 3 pointers. They score 130 points. How many 2 point and 3 point baskets were made?
Answer by macston(4006) (Show Source):
You can put this solution on YOUR website! .
x=number of two point goals; y=number of three point goals
.
x+y=51
y=51x
.
2x+3y=130
2x+3(51x)=130
2x+1533x=130
153x=130
23=x
ANSWER 1: They made twenty three 2 point baskets.
.
y=51x=5123=28
ANSWER 2: They made twenty eight 3 point baskets
.
CHECK:
2x+3y=130
2(23)+3(28)=130
46+84=130
130=130
Question 991371: What is the value of x and z when given the following degrees: (8x3), 77 and z
Answer by Fombitz(25151) (Show Source):
Question 991496: Solve by elimination
2x4yz=8
3x+2y+z=6
5x2y+3z=3
Answer by solver91311(20879) (Show Source):
You can put this solution on YOUR website!
Add the first two equations to eliminate z. Then add the result to the third equation and get the absurdity 0 = 17. The system is inconsistent.
John
My calculator said it, I believe it, that settles it
Question 991350: 7x – 4y = –7
5x + y = 22
Answer by macston(4006) (Show Source):
You can put this solution on YOUR website! .
What exactly is your question?
.
5x+y=22
y=225x
.
7x–4y=–7
7x4(225x)=7
7x88+20x=7
27x=81
x=3
.
5x+y=22
5(3)+y=22
15+y=22
y=7
.
Possible answer: (3,7)
Question 991058: A gym charges a one time joining fee of $50 and then a monthly membership fee of $25.
Write a function to represent the situation and define the variables.
Answer by Alan3354(47455) (Show Source):
Question 990964: Please help me solve this equation: 3x+2y=25
x3y=1
Answer by ikleyn(988) (Show Source):
You can put this solution on YOUR website! .
.
Express x from the second equation, x = 3y+1, and substitute it into the first equation. You will get the equation for a single unknown y:
3*(3y + 1) + 2y = 25.
Simplify and solve it:
9y + 3 + 2y = 25,
11y = 25 3,
11y = 22.
Please complete the solution yourself.
Question 990978: Please help me solve this equation: y=2x+3
4x+2y=12
Answer by ikleyn(988) (Show Source):
You can put this solution on YOUR website! .
.
Simply substitute the expression for y from the first equation to the second one. You will get
4x + 2*(2x+3) = 12.
Simplify it:
4x  4x + 6 = 12.
6 = 12.
Could it be so? No.
It means that your system has no solution.
Geometrically the original equations represent two parallel straight lines in a coordinate plane that have no intersection  have no common point.
Question 990987: Is 9x+11zy=12y linear? And write it in standard form
Answer by Edwin McCravy(13211) (Show Source):
Question 990973: Please help me solve this equation: 2x+y=10
2x+2y=16
Answer by josgarithmetic(13975) (Show Source):
Question 990636: can you help me solve this please thanks?
x+yz=0
2xy+z=3
x+5y3z=2
Answer by solver91311(20879) (Show Source):
You can put this solution on YOUR website!
Since you didn't specify a method, here is GaussJordan row reduction.
1 1 1 0
2 1 1 3
1 5 3 2
1 1 1 0 2R1 + R2 to R2
0 3 3 3
1 5 3 2
1 1 1 0 R1 + R3 to R3
0 3 3 3
0 6 4 2
1 1 1 0 R2/3 to R2
0 1 1 1
0 6 4 2
1 1 1 0 6R2 + R3 to R3
0 1 1 1
0 0 2 8
1 1 1 0 R3/2 to R3
0 1 1 1
0 0 1 4
1 1 0 4 R3 + R1 to R1
0 1 1 1
0 0 1 4
1 1 0 4 R2 + R1 to R1
0 1 0 3
0 0 1 4
1 0 0 1 R3 + R2 to R2
0 1 0 3
0 0 1 4
John
My calculator said it, I believe it, that settles it
Question 990672: Suppose a devastating freeze destroyed roughly 85% of California Central Valley's orange crop. As a result of the freeze, an orange that cost $0.50 before the freeze would cost $1.50 after the freeze. Model the price c of an orange as a linear function of the percentage p of the crop that was destroyed. (Hint: When 0% of the crop was destroyed, the price was $0.50.)
Answer by josgarithmetic(13975) (Show Source):
You can put this solution on YOUR website! You want ordered pair points as (percentDamaged,price). Two points you have are (0,0.5) and (85,1.5), which you may assign coordinate variables as (p,c).
Notice that one of these points is the caxis intercept! Feed everything into slopeintercept form and simplify:
Question 990739: How do you simplify the quadratic 3x^2+3x6=0 into 2 binomials?
Found 2 solutions by MathLover1, Boreal: Answer by MathLover1(11324) (Show Source): Answer by Boreal(1464) (Show Source):
Question 990655: If X+y+z=112 and y=4x and z=11y then find the value of y
Answer by ikleyn(988) (Show Source):
Question 990423: 3, 5 is on the graph of 3x + 5 y equals 30 tell whether the statement is true or false and justify your answer
Answer by Boreal(1464) (Show Source):
Question 990347: Describe two applications for graphing linear equations
Answer by josgarithmetic(13975) (Show Source):
You can put this solution on YOUR website! Would you narrow that a bit? Too too many applications. Check in your textbook about applications, included with many exercise sets and often in separate Applications sections of the books.
A very common academic exercise is ticket sales, numbers of types of tickets, and the revenue.
Question 990022: Make up a pair of linear equations with solution: x = 6 and y = 10.
Answer by stanbon(69061) (Show Source):
You can put this solution on YOUR website! Make up a pair of linear equations with solution: x = 6 and y = 10.

2x = 12
3y = 30

1st Equation: 3y+2x = 42

5x = 30
2y = 20

2nd Equation:: 2y5x = 10

Cheers,
Stan H.


Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790, 11791..11835, 11836..11880, 11881..11925, 11926..11970, 11971..12015, 12016..12060, 12061..12105, 12106..12150, 12151..12195, 12196..12240, 12241..12285, 12286..12330, 12331..12375, 12376..12420, 12421..12465, 12466..12510, 12511..12555, 12556..12600, 12601..12645, 12646..12690, 12691..12735, 12736..12780, 12781..12825, 12826..12870, 12871..12915, 12916..12960, 12961..13005, 13006..13050, 13051..13095, 13096..13140, 13141..13185, 13186..13230, 13231..13275, 13276..13320, 13321..13365
