Question

HELP! I NEED THE ANSWER ASAP!!!!!

Use the linear combination method to solve the system of equations. Explain each step of your solution.

2x + y = −6

−8x + 2y = 12

Answer 1

The solution to the given system of equations is (-2, -2).

Explanation:

The given system of equations is,

2x + y = -6 .......(1)

-8x + 2y = 12 ......(2)

Now, we will make the coefficients of either x or y as opposites.

In the above system of equations, we will make the coefficients of x as opposites.

Multiplying equation (1) by '4' and equation (2) by '1', we get

8x + 4y = -24 .......(3)

-8x + 2y = 12 .......(4)

Now, we will add the equations (3) and (4).

(8x + 4y) + (-8x + 2y) = -24 + 12

⇒8x + 4y - 8x + 2y = -12

⇒6y = -12

⇒y =
`(-12)/(6)`

⇒y = -2

Now, substituting the value of y in equation (1), we get

2x + (-2) = -6

⇒2x - 2 = -6

⇒2x = -6+2

⇒2x = -4

⇒x =
`(-4)/(2)`

⇒x = -2

∴ x = -2; y = -2 is the solution of the given system of equations.