Equation A=8x-6y=-20 Equation B=-16x+7y=30

The two equations represent a system of linear equations. What is the solution to this system of linear equations

A: (-2,-1) B: (1,2)

C: (-1,2) D: (2,-1)

C: (-1,2)

Step-by-step explanation:

This is a system of linear equations and can be solved by elimination method.

Step 1

A=8x-6y=-20

B=-16x+7y=30

Multiply equation A by 7 and equation B by - 6

7A=56x-42y=-140

-6B=96x-42y=-180

Step 2

Eliminate the term that has y by subtracting each term in equation A from each corresponding term in equation B

40x=-40

Step 3

Divide both sides of the equation by 40, the coefficient of x in order to find the value of x

40x/40=-40/40

x=-1

Step 4

Put x=-1 in equation B

B=-16x+7y=30

-16 (-1) + 7y=30

16+7y=30

Step 5

Collect like terms by subtracting 16 from both sides

16+7y-16=30-16

7y=14

Step 6

Divide both sides of the equation by 7, the coefficient of y

7y/7=14/7

y=2

Therefore, the solution to the system of equations is

(-1, 2)