The linear combination method gives a solution of (–4, 2) for which of these systems of linear equations?

the first set of equation. you check (-4,2) by plugging in -4 for x and 2 for y to see they hold:

3*(-4)+13*2=14

6*(-4)+11*2 = -2

presumably all methods would give the same solution; for each choice we just try x=-4, y=2 and see if it checks.

a.

3x+13y=3(-4)+13(2)=-12 + 26 = 14   that checks

6x+11y=6(-4)+11(2)=-24 + 22 = -2 that checks too

b.  

4x + 5y =4(-4)+5(2)=-16 + 10 = 6   nope

c.

5x+4y = 5(-4)+4(2)=-20 + 8= -12 nope

d.

10x+3y = 10(-4)+3(2)=-40 + 6 = -34 nope

answer: a (the first one) is correct