Question

Solve the following system of equations by linear combination:

3x – y = 7

x + y = 5

Answer 1

Explanation:

that means we optionally multiply one or both equations with some factors, so that one variable term has the same coefficient in both equations but with different signs.

and then we add both equations giving us one equation in the other variable, which we can solve.

and then we use that with any of the original equations to solve for the first variable.

in this case we don't need the multiplication step, as the terms in y have already the same coefficient (1) with different signs.

so, we add both equations

3x - y = 7

+ x + y = 5

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4x 0 = 12

4x = 12

x = 12/4 = 3

x + y = 5

3 + y = 5

y = 5 - 3 = 2

Answer 2

x=3, y=2

Explanation:

First Add both equations

3x-y=7 ---1

x+y=5 ---2

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so we get, 4x=12

so x=3

Now plug x back into equation 2 so we get y=2