Question

Solve by the linear combination method (with or without multiplication).

Answer 1

The first step is to name the equations to make the process of solving them easy.

$6x+7y=-4....(1)\\5x-3y=-21....(2)$

The second step is to multiply  each of the equations by the coefficient of the x term in the other equation. In this case, we will multiply equation  (1) by 5 to get equation (3) and then multiply equation (2) by 6 to get equation (4).

$-30x-35y=20...(3)\\30x-18y=-126...(4).$

The next step is to add equation equation(3) and  (4) together to get equation (5) as shown below;

$-53y=-106....(5)\\=> y= 2.$

The next step is to take the value of y and substitute it into any of the equations above.  For this solution, I pick equation (1). The work done to solve for x is shown below.;

$6x+7y=-4\\=>6x+7(2)=-4\\=>6x=-18\\=>x=-3$

The solution for this system of equations is $(-3,2)$