# Questions on Algebra: Systems of equations that are not linear answered by real tutors!

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Question 993472: The sum of two numbers is 66. Their difference is 8.
Write in system of equations
Can someone help me please

Found 2 solutions by MathTherapy, rothauserc:
Answer by MathTherapy(4047)   (Show Source):
You can put this solution on YOUR website!
The sum of two numbers is 66. Their difference is 8.
Write in system of equations
Can someone help me please
Let larger number be L, and smaller, S
We then get:
Add the 2 equations to ELIMINATE S, and to determine L, the larger number
Substitute the value for L in any of the 2 equations to find the value of S, the smaller number



Answer by rothauserc(2272)   (Show Source):
You can put this solution on YOUR website!
x + y = 66
x - y = 8
*******************************************
solve second equation for x
x = y + 8
substitute for x in first equation
y+8 +y = 66
2y = 58
y = 29
*******************************************
x - 29 = 8
x = 37
******************************************
x = 37 and y = 29

Question 993214: A boat travels 48 miles upstream in 6 hours. Going down stream it can travel 72 miles in the same amount of tume. Find the speed of the current and speed of the boat in still water
Answer by lwsshak3(11500)   (Show Source):
You can put this solution on YOUR website!
A boat travels 48 miles upstream in 6 hours. Going down stream it can travel 72 miles in the same amount of tume. Find the speed of the current and speed of the boat in still water
let x=speed of boat in still water
let c=speed of current
(x+c)=speed of boat downstream
(x-c)=speed of boat upstream
travel time*speed=distance
6*(x+c)=72
6*(x-c)=48
6x+6c=72
6x-6c=48
12x=120
x=10
6c=72-60
6c=12
c=2
speed of boat in still water=10 mph
let c=speed of current=2 mph

Question 992662: F varies directly with m and inversely with the square of D
If F=150 when m=240 and d=8, find F when m=360 and d=3.

Answer by rothauserc(2272)   (Show Source):
You can put this solution on YOUR website!
we use k as the constant of proportionality, then
F = mk / d^2
we are given F = 150, m = 240, d = 8
150 = 240k / 8^2
240k = 9600
k = 40
*************************************
our formula becomes
F = 40m / d^2
we are given m=360, d= 3
F = (40*360) / 3^2
F = 1600

Question 992514: A=r/2L solve for L
Answer by Timnewman(249)   (Show Source):
You can put this solution on YOUR website!
Hi dear,
If A=r/2L
Then,multiply out to get
r=2AL
Divide bothside by 2A,
Then,
L=r/2A
HOPE THIS HELPS?
::TIMNEWMAN::

Question 992073: 2y+6xy=z. solve for y
Answer by jim_thompson5910(33401)   (Show Source):
You can put this solution on YOUR website!

Factor out y

Divide both sides by .

Question 991036: Write the verbal translation of the formula
For converting temperature from Celsius (C) to Fahrenheit (F) which is F=5/9C+32

Answer by Cromlix(3061)   (Show Source):
You can put this solution on YOUR website!
Hi there,
The Celsius reading.
Multiply this value by 9.
Finally divide the answer by 5.
Add 32 to reading.
°C x 9/5 + 32 = °F
Hope this helps. :-)

Question 990196: What's the solution to -5x+2y=-10 and 3x-6y=-18
Answer by Fombitz(25151)   (Show Source):
You can put this solution on YOUR website!
Multiply the first equation by 3 and add to the first to eliminate .

Now use either equation to solve for .

Question 990395: Formulate a system of equations for the situation below and solve.
A theater has a seating capacity of 834 and charges $3 for children,$5 for students, and $7 for adults. At a certain screening with full attendance, there were half as many adults as children and students combined. The receipts totaled$4346. How many children attended the show?

Answer by macston(4006)   (Show Source):
You can put this solution on YOUR website!
.
C=number of children. S=number of students, A=number of adults
.
(1/2)(C+S)=A
C+S=2A Use this to substitute for (C+S)
.
C+S+A=834
(C+S)+A=834 Substitute for (C+S)
2A+A=834
3A=834
A=278 .
278 Adults attended the show.
Receipts from adults=($7)(278)=$1946
Receipts from students and children=$4346-$1946=$2400 . C+S=834-278 C+S=556 C=556-S Use this to substitute for C .$3C+$5S=$2400 Substitute for C.
$3(556-S)+$5S=$2400$1668-$3S+$5S=$2400$2S=$732 S=366 366 Students attended the show. . C=556-S=556-366=190 ANSWER: 190 children attended the show. . CHECK: C+S+A=834 190+366+278=834 834=834 .$3C+$5S+$7A=$4346$3(190)+$5(366)+$7(278)=$4346$570+$1830+$1946=$4346$4346=$4346 . Question 990344: 2x+y=-5,3x+2y=-8 Answer by stanbon(69061) (Show Source): You can put this solution on YOUR website! 2x+y=-5 3x+2y=-8 ---- Modify for elimination: 4x + 2y = -10 3x + 2y = -8 ------ Subtract and solve for "y":: x = -2 --- Solve for "y":: 2x + y = -5 -4 + y = -5 y = -1 ----------- Cheers, Stan H. ----------- Question 990349: 6a+3b=4,a+b=1 Answer by Boreal(1464) (Show Source): You can put this solution on YOUR website! 6a+3b=4 a+b=1 b=1-a substitute into first equation 6a+3(1-a)=4 6a+3-3a=4 3a=1 a=(1/3) b=(2/3) 6*(1/3)=2 3*(2/3)=2 and 6a+3b=4 Question 990114: -13 + x = -25 Answer by jim_thompson5910(33401) (Show Source): You can put this solution on YOUR website! -13 + x = -25 -13 + x + 13 = -25 + 13 ... Add 13 to both sides. x = -12 Question 989339: Certain chemotherapy dosages depend on a patient's surface area. According to the Mosteller model S = √(h*M) / 6 where h is the patient's height in m, M is the patient's mass in kg and S is the patient's approximate surface area in m^2. Assume that the patient's height is a constant 187 cm but he is on a diet. If a patient loses 3.1 kg per month, how fast is his surface area changing (in m^2/month) at the instant his mass is 71 kg? Give your answer correct to 4 decimal places. Note. You may be wondering why we have referred to the patient's mass here, rather than his weight. Technically, a person's weight is a force (recall: F = Ma, where F is the force, M is the mass, and a is the acceleration, which in this case is g, the acceleration due to gravity). Force (and therefore weight) is measured in Newtons, not kilograms. Scientists, and you are one, should know that. (In orbit, an astronaut experiences weightlessness, not masslessness.) - I am not sure why this matters? I am so confused! Initial = S = √(187*71) / 6 = 19.2043 After One month = S = √(187*69.7) / 6 = 19.0277 I am not sure how to put these together? THANK YOU Found 2 solutions by jim_thompson5910, MathLover1: Answer by jim_thompson5910(33401) (Show Source): You can put this solution on YOUR website! Let x = mass in kilograms S(x) = body surface area in square meters. This is a function of x. The height is constant at 187 cm = 1.87 meters. So is our surface area function (in square meters). ------------------------------------------------------- Take the derivative of S(x) with respect to t (time). Doing so gives you Plug in x = 71 (given mass) and (the amount of mass being lost per month) So the surface area is changing at an instantaneous rate of approximately -0.04192490398719 square meters per month when the mass is 71 kg. Answer by MathLover1(11324) (Show Source): You can put this solution on YOUR website! Since height is constant, differentiate with respect to mass: => Question 988745: 8-(-9) Answer by jim_thompson5910(33401) (Show Source): You can put this solution on YOUR website! Two negatives make a positive. Subtracting a negative is the same as adding the positive version of it 8-(-9) = 8 + 9 = 17 Question 988534: 4x+y=14 and y=3x solution Answer by macston(4006) (Show Source): You can put this solution on YOUR website! . y=3x Use this to substitute for y . 4x+y=14 Substitute for y 4x+3x=14 7x=14 x=2 . y=3x Put in value for x y=3(2) y=6 . ANSWER: (2,6) . CHECK: 4x+y=14 4(2)+6=14 8+6=14 14=14 Question 988444: -6(a+8) Answer by jim_thompson5910(33401) (Show Source): You can put this solution on YOUR website! Multiply the outer -6 by each term inside. So -6 times 'a' is -6a. Also, -6 times +8 is -48 In the end, -6(a+8) distributes to -6a-48 Question 988348: place the number 1-9 in the squares so that none of the rows, columns, or diagonals have the same sum. Plz help Answer by solver91311(20879) (Show Source): You can put this solution on YOUR website! What squares? John My calculator said it, I believe it, that settles it Question 988350: joey dumped the change out of his pocket and found that he had 25 coins totaling exactly$1.00 what coins might joey have had in his pocket? Plz help
Answer by solver91311(20879)   (Show Source):
You can put this solution on YOUR website!

First thing to note is that you must have some pennies. That is because if you had all nickels, you would only have 20 coins.

Second, you must have a number of pennies that is divisible by 5, because if you have some number of pennies NOT divisible by 5, you can't get to an even dollar no matter how many coins you have.

Third, you can't have as many as 25 pennies, because that would account for all 25 coins, but you only have 25 cents.

So, let's examine the situation if you have 20 pennies. That means that you would have to make 80 cents from 5 coins consisting of quarters, dimes, and nickels.

Is it possible to do this if you have zero quarters? No, because the most you can have with five coins if none of them are quarters is 50 cents, but we need 80 cents.

Is it possible to do this if you have one quarter? No, because 80 minus 25 is 55, and the most you can have is 40 if the remaining four coins are dimes.

Is it possible to do this if you have three quarters? No, because 80 minus 75 is 5, and there is no way to make 5 cents with two coins.

So far we have proven that if 20 of the coins are pennies, then two of the other coins must be quarters. I sense we are tantalizingly close to a solution here.

I'll let you finish. Let me know what you come up with.

By the way, there are also solutions that have 15 or 10 pennies.

John

My calculator said it, I believe it, that settles it

Question 988346: To find a baseball pitcher's earned run average (ERA), you can use the formal Ei= 9r, in which E represents ERA, i represents the number of innings pitched, and r represents the number of earned runs allowed. Solve the equation for E. What is a pitcher's ERA if he allows 5 earned runs in 18 innings pitched?
Answer by macston(4006)   (Show Source):
You can put this solution on YOUR website!
.

.
ANSWER: His ERA is 2.5.

Question 988291: Simplify using order of operations
(9)(2)+3(15-5)-8

Answer by EdenWolf(454)   (Show Source):
You can put this solution on YOUR website!

Multiply 9 and 2 first.

Subtract 5 from 15.

Multiply 3 and 10.

Add 18 and 30.

Subtract 8 from 48.
The answer is .

Question 988328: g(h+2/3)=1 for h
Answer by solver91311(20879)   (Show Source):
You can put this solution on YOUR website!

Do you mean

Or

John

My calculator said it, I believe it, that settles it

Question 988068: A=FV-OV/T for OV (How do I solve it)?
Answer by Fombitz(25151)   (Show Source):

Question 988034: A=FV-OV/T for OV
Answer by stanbon(69061)   (Show Source):
You can put this solution on YOUR website!
A=FV-OV/T for OV
-------
Multiply thru by "T" to get:
-------
AT = FVT - OV
-------
OV = FVT - AT
-----
OV = (FV-A)T
-----------
Cheers,
Stan H.
----------

Question 988036: A student was asked to use the formula for the perimeter of a rectangle, P=2L+2w, to solve for L. The student came up with an answer, P-2w=2L. What error did the student make? Explain. Then solve for L.
Answer by josgarithmetic(13975)   (Show Source):
You can put this solution on YOUR website!
This student took just one step, a good one; and then stopped. He just did not finish.

Question 988041: A=FV-OV/T for OV
Answer by josgarithmetic(13975)   (Show Source):
You can put this solution on YOUR website!
Multiplication Property of Equality;
Addition Property of Equality;
Multiplication Property of Equality;

Question 988035: C=Wtc/1000 for W
Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
C=Wtc/1000 for W
============
Multiply both sides by 1000
Divide by tc

Question 987953: 2(x+y)+y
Answer by vleith(2950)   (Show Source):

Question 987802: Solve the system of equations x+y=2 and x^2+2y^2=11
Answer by ikleyn(988)   (Show Source):
You can put this solution on YOUR website!
.
Solve the system of equations

.
-----------------------------

Express x from the first equation  x = 2-y  and substitute it into the second equation.  You will get

+ = ,

+ - = 0,

= ,

= = = = .

= = = ;

= = = -1.

Question 987464: Alexa and Zack are solving the following problem: The number of miles on Car A is 50 miles more than the number of miles on Car B, and the number of miles on Car B is 30 miles more than the number of miles on Car C. All the cars travel 50 miles in 1 hour. After 1 hour, twice the number of miles Car A is 70 miles less than 3 times the number of miles on Car C. How many miles were there on Car B initially? Alexa assumes there are m miles on Car B. Zack assumes there are m miles on Car C. Will Zack's answer be the same as Alexa's answer? Explain.
Answer by ankor@dixie-net.com(18980)   (Show Source):
You can put this solution on YOUR website!
Alexa and Zack are solving the following problem:
The number of miles on Car A is 50 miles more than the number of miles on Car B,
a = b+50
and the number of miles on Car B is 30 miles more than the number of miles on Car C.
b = c+30
or
c = b-30
All the cars travel 50 miles in 1 hour.
All travel at 50 mph
After 1 hour, twice the number of miles Car A is 70 miles less than 3 times the number of miles on Car C.
2(a+50) = 3(c+50) - 70
2a + 100 = 3c + 150 - 70
2a = 3c + 150 - 70 - 100
2a = 3c - 20
Replace a with (b+50), replace c with (b-30)
2(b+50) = 3(b-30) - 20
2b + 100 = 3b - 90 - 20
2b + 100 = 3b - 110
2b = 3b - 110 - 100
2b = 3b - 210
210 = 3b - 2b
b = 210 mi car B initially
then
a = 210 + 50
a = 260 car A initially
and
c = 210 - 30
c = 180 mi Car C initially

Alexa assumes there are m miles on Car B.\
Zack assumes there are m miles on Car C.
Will Zack's answer be the same as Alexa's No

Question 987501: x-2y=1 solve for y
literal equations

Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
x-2y=1 solve for y
===============

===================
Is there some reason you couldn't do that?
It's basic. Things are gonna get more difficult.

Question 987231: y=x+6;(-5,11) tell weather the equation has the given ordered pair as a solution.
Answer by macston(4006)   (Show Source):
You can put this solution on YOUR website!
.
y=x+6
11=-5+6
11=1 FALSE
ANSWER: The ordered pair is not a solution.

Question 986894: Four numbers are such that the second number is 4 less than 3 times the first number and the third number is a quarter of the second number. The fourth number is five more than the first number. Determine the value of these four numbers if their sum is 115.
Answer by Timnewman(249)   (Show Source):
You can put this solution on YOUR website!
Hi dear,
Let the 1st number be a,
2nd =b
3rd=c
4th=d
From your question,
b=3a-4---(1)
c=b/4----(2)
d=5+a----(3)
From equ 1,
a=(b+4)/3---(4)
Put 4 in 3,
d=5+(b+4)/3--(5)
If the sum of a,b,c,d is 115,
Then,

Take the L.c.m and get
23b+92=1380
23b=1380-92
23b=1288
b=56
Put b=56 in equ 2,4,5, and get;
a=20,
c=14,
d=25
So the values of the fisrt,second,third,and fourth numbers are;20,56,14,and 25 respectively.
HOPE THIS HELPS?
Best wishes,
Timnewman::

Question 986858: What is the answer to 20-2(2 x 6)+8 divided by 4=

Answer by farohw(153)   (Show Source):

Question 986292: Find the sum of a squared number and seven
Answer by Fombitz(25151)   (Show Source):

Question 985971: Find two numbers that add to 3 and multiply to -40.
(Enter the two numbers separated by a semicolon.)
Thanks

Answer by ikleyn(988)   (Show Source):
You can put this solution on YOUR website!
.
You need to find two integers  x  and  y  from the system of two equations in two unknowns

.

Express  y  from the first equation  y = 3 - x  and substitute it to the second equation.  You will get

x*(3 - x) = -40.

Solve it:

+ + = ,

- - = ,

The roots are  x = 8  and  x = -5   (use the quadratic formula).

From the first equation,  if  x = 8  then  y = -5.
Similarly,  if  x = -5,  then  y = 8.

Answer.  The pairs  (8,-5)  and  (-5,8)  are the solutions.

Question 986027: Find two numbers that add to 3 and multiply to -40.
(Enter the two numbers separated by a semicolon.)
Thanks.

Found 2 solutions by macston, Alan3354:
Answer by macston(4006)   (Show Source):
You can put this solution on YOUR website!
.
x and y are the two numbers
.
x+y=3
x=3-y Use this to substitute for x.
.
Substitute for x from above.

OR
OR
If y=8, x=-5; if y=-5,x=8
ANSWER The two numbers are 8 and -5.

Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
Find a pair of factors of 40 that differ by 3.

Question 985922: y=x^2-10
9x^2-y^2=90
The solution set is?

Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(11324)   (Show Source):
You can put this solution on YOUR website!

----------------

----------------

----------------

----------------

----------------
if left sides same, then we have

............square both sides

.....both sides multiply by

....factor

zeros:

if =>=> or
if =>=> or
approximately:
or
or

for => => =>
for => => =>
for =>=>=>=> and =>
for =>=>=>=>
check:

Answer by ikleyn(988)   (Show Source):
You can put this solution on YOUR website!
.
.

Substitute   = -   from the first equation into the second equation.  You will get

- = .

Solve it:

- () = ,

- + - = ,

- + = .

It is a bi-quadratic equation.     Don't be afraid !     Don't panic !

The Math gives you an opportunity to demonstrate your skills ! :)

Introduce new variable   = .

Then you will get quadratic equation

- + = .

Its roots are  (use the quadratic formula)

= 19, = 10.

Hence,   = +/-, +/-.

Then from the first equation of the system

y = - = 19 - 10 = 9   OR   y = 10 - 10 = 0.

Answer.  The solutions are the pairs  (x,y) = (, ),  (, ),  (, )  and  (, ).

Question 985690: 4 culiques cost as much as 3 thingabobs
5 thingabobs cost as much as 6 whatsits.
What's the cost of 5 culiques and the cost of 4 whatsits?

Answer by macston(4006)   (Show Source):
You can put this solution on YOUR website!
.
4 culiques=3 thingabobs
1 culique=3/4 thingabob
.
6 whatsits=5 thingabobs
1 whatsit=5/6 thingabob
.
5 culiques=5(3/4 thingabob)=15/4 thingabobs
.
4 whatsits=4(5/6 thingabob)=20/6 thingabobs

Question 985453: Z z varies jointly as the square root of the product of x and y. if z = 3 when x = 3 and y = 12, find x when z = 6 and y = 64
Answer by josgarithmetic(13975)   (Show Source):
You can put this solution on YOUR website!
Put the description into algebraic or arithmetic symbolism.

Solve for k and substitute the given values to evaluate k.

Question 985451: Q varies jointly as r and s. If q= 2.4m when r =0.6 and s= 0.8, find q when r= 1.6 and s=.01.
Answer by stanbon(69061)   (Show Source):
You can put this solution on YOUR website!
Q varies jointly as r and s.
Q = k*r*s
-------------------
Solve for "k" using "If q= 2.4m when r =0.6 and s= 0.8"
2.4 = k*0.6*0.8
----
2.4 = 0.48k
k = 2.4/0.48
k = 5
-------
Find q when r= 1.6 and s=.01.
Q = 5*1.6*0.01
Q = 0.08
====================
Cheers,
Stan H.
------------

Question 985328: what is the degree of x-8=0?

Answer by Boreal(1464)   (Show Source):
You can put this solution on YOUR website!
The degree is 1, x^1-8=0. It is the variable with the greatest exponent.

Question 985276: If y = 7 / (8 x + 1)
what is the y-intercept of its graph?

Answer by josgarithmetic(13975)   (Show Source):
You can put this solution on YOUR website!

Just evaluate this.

JUST EVALUATE THAT! COMPUTE THE EXPRESSION.