solve the system using elimination.

Question

-6x+3y=-6, -3x+5y=-38

Answer 1

Elimination method

Given equations -6x+3y = -6 ----> (1)

-3x+5y = -38 ------> (2)

Multiple to each side by  2.

6x-10y = 76 ------> (3)

To eliminate the x value,add the equatiions (1) & (3).

-6x+10y = -76

-6x+3y = -6

(+)  (-)    (+)

__________

7y = -70

Divide to each side by 7.

7y/7 = -70/7

⇒ y = -10

Substitute y = -10 in equation (1).

-6x+3*-10 = -6

-6x- 30 = -6

Add 30 to each side.

-6x-30+30 = -6+30

-6x = 24

Divide to each side by negitive 6.

-6x/-6 = 24/-6

⇒ x = -4

Check

Substitute x,y in equation (2).

-3*-4+5*-10 = -38

12-50 = -38

-38 = -38

Comments

- 38 = - 38. The above statement is true. So, (x, y) = (- 4, - 10) is the solution of the given system.