SOLUTION: I need help, this problem deals with the substitution method. Your help will be greatly appreciated. x + y = 20 30x + 25y = 550

Question 134113: I need help, this problem deals with the substitution method. Your help will be greatly appreciated.
x + y = 20
30x + 25y = 550
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given system of equations:

Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.

So let's isolate y in the first equation

Start with the first equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

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

Since , we can now replace each in the second equation with to solve for

Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute to

Multiply

Combine like terms on the left side

Subtract 500 from both sides

Combine like terms on the right side

Divide both sides by 5 to isolate x

Divide

-----------------First Answer------------------------------

So the first part of our answer is:

Since we know that we can plug it into the equation (remember we previously solved for in the first equation).

Start with the equation where was previously isolated.

Plug in

Multiply

Combine like terms

-----------------Second Answer------------------------------

So the second part of our answer is:

-----------------Summary------------------------------

So our answers are:

and

which form the point

Now let's graph the two equations (if you need help with graphing, check out this solver)

From the graph, we can see that the two equations intersect at

. This visually verifies our answer.

graph of (red) and (green) and the intersection of the lines (blue circle).

RELATED QUESTIONS
Hi I really need help with this problem. Use the substitution method to solve Y=-2X-4 (answered by Alan3354)

I need help solving this problem by graphing 2x-y=4 and 2x-y=6 this problem your help... (answered by stanbon,MathLover1)

how do i solve this system by the substitution method? x-2y = 4 y=3x-22 any help... (answered by TimothyLamb)

I'm sturggling with this problem. Any help would be greatly appreciated. Solve the... (answered by stanbon,checkley71)

I am trying to figure out how to solve this problem using the substitution method. I know (answered by ewatrrr)

I need help with a solve by substitution method equation< the answer should be an ordered (answered by ewatrrr)

This problem deals with the addition method, and I need help. 2a + 3b = -1 3a + 5b = (answered by checkley71,nycsharkman,solver91311)

Given f(x)=X^2+3 find and simplify the difference quotient [f(x+h)-f(x)]/h I know I need (answered by Alan3354,mananth)

Hello, I've been trying to solve this problem but am stuck. Solve by Substitution... (answered by Alan3354)