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

6x + 7y = –4
5x – 3y = –21

User Akhtar
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1 Answer

1 vote

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)


User Gfredericks
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