Solving for systems of equation using the elimiation method.

Question

3x-2y=x-6
3(x+2y)=3

Answer 1

3x - 2y = x - 6
3(x + 2y) = 3

Lets rearrange the second equation
3(x + 2y) = 3
x + 2y = 1

Now you have:
3x - 2y = x - 6
x + 2y = 1

You want to eliminate one variable and the easiest one to do so is y. So add the two equations together like so..

3x - 2y + x + 2y = x - 6 + 1

Simplify..

4x = x - 5
3x = -5
x = -5/3

Plug back into one of the original equation and solve for y..

3(-5/3) - 2y = -5/3 - 6
-5 - 2y = -5/3 - 6
2y = 5/3 + 1
y = 4/3

So x is -5/3 and y is 4/3.

Answer 2

thank you for your response.

I should have included the answers the book gives.

It gives X=-7 Y=4

Answer 3

That's not possible. x and y are the same for both those equations. Although x = -7 and y = 4 does satisfy the second equation it does not for the first one.

3x - 2y = x - 6
3(-7) - 2(4) = -7 - 6
-21 - 8 = -7 - 6
-29 = -13 ??? This is not possible so those two values cannot be x and y. Are you sure you typed the equations right? A way for the x = -7 and y = 4 to be true is if the first equation is 3x + 2y = x - 6. So it may be a typo by the book *shrug*.