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use the linear combination method to solve the system of equations. explain each step of your solution.

2x + y = −6

−8x + 2y = 12

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

Step-by-step 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 =

⇒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 =

⇒x = -2

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

step-by-step explanation:

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step-by-step explanation: