Question

Elimination

x+2y=2
-x+3y+13

Answer 1

We're given two equations.

Equation 1 is : x + 2y = 2

Equation 2 is : - x + 3y = 13

Since both equations just have "x" in it, we can already jump right into solving! 

Since x, y, and regular numbers are lined up, we can very simply add the equations to each other.

     x + 2y = 2

  - x + 3y = 13

    0 + 5y = 15

We now have this :

5y = 15

So, let's divide both sides by 5.

$\dfrac{5\text{y}}{5} = \dfrac{15}{5}$

Simplify.

y = 3

So, now that we have this value for y, we can plug in 3 for y in our very first equation...

Equation 1 : x + 2y = 2

x + 2·(3) = 2

Simplify.

x + 6 = 2

Subtract 6 from both sides.

x + 6 - 6 = 2 - 6

Simplify.

x = - 4

So, the answers are :

x = -4, y = 3