SOLUTION: I am trying to learn the substitution method. I do not understand the steps. Here is my problem; 2x-3y = 12 x = 4y + 1

Question 129270: I am trying to learn the substitution method.
I do not understand the steps.
Here is my problem;
2x-3y = 12
x = 4y + 1
Found 2 solutions by brikay0299, jim_thompson5910:
Answer by brikay0299(3) (Show Source): You can put this solution on YOUR website!
2x-3y=12 x=4y+1 you would add what x equals in the place of x and solve
2*4y+1-3y=12 take all the numbers with letters next to it and add,subtract,divide,or multiply the numbers 2*1y+1=12 then drop the one and it just becomes y now add the numbers 2 and 1 that would become 3y=12 now divide each side by 3 to get rid of the 3 next to y cause dividing number will cause multiplication to cancel it out come up with answer 4
check answer
2x-3y=12 3*4=12
2*4y+1-3y=12
2*y+1=12
3y=12
3y/3=12/3
y=4

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given system

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

Combine like terms on the left side

Subtract 2 from both sides

Combine like terms on the right side

Divide both sides by 5 to isolate y

Divide

Now that we know that , we can plug this into to find

Substitute for each

Simplify

So our answer is and which also looks like

Notice if we graph the two equations, we can see that their intersection is at . So this verifies our answer.

Graph of (red) and (green)

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