Question

Solve system using elimination
-5x + 3y = 2 for x
-5x - 5y = -30 for y

Answer 1

Equation 1 : -5x + 3y = 2

Equation 2 : -5x - 5y = -30

Because both equations contain a like term (which in this case is 5x), we can easily subtract these equations from one another.

Subtract equation 1 from equation 2 :

-5x - (-5x) = 0

3y - (-5y) = 3y + 5y $\rightarrow$ 8y

2 - (-30) = 2 + 30 $\rightarrow$ 32

This leaves us with 8y = 32. Simplify this to get y by dividing both sides by 8.

8y ÷ 8 = 32 ÷ 8

Simplify.

y = 4

Now, plug in 4 for y in our first equation.

-5x + 3(4) = 2

Simplify.

-5x + 12 = 2

Subtract 12 from both sides.

-5x = 2 - 12

Simplify.

-5x = -10

Divide both sides by -5.

-5x ÷ -5 = -10 ÷ -5

Simplify.

x = 2

Therefore, our answer is :

(2, 4) where x = 2, y = 4