-x+y=6

3x-y=2

the combination method addds these equations together.

-x+y=6

3x-y=2

———

(-x+3x) + (y-y) = (6+2)

2x + 0 = 8

2x=8

x=4

plug that into one of the equations

-(4)+y=6 or 3(4)-y=2

y=10 or 12-y=2…. y=10

The first problem is much the same, but if we just add them, the y’s will not cancel nor will the x’s. usually we’d just multiple all the terms in the second equation by -2 so we can cancel the x’s. But look what happens when we do that:

2x+6y=8

-2(x+3y)=-2(2)

2x+6y=8

-2x-6y=-4

————-

(2x-2x)+(6y-6y)=(8-4)

0+0=4 ?!?!?

The lines are parallel. They do not intersect. Put the lines into the y=mx+b form:

2x+6y=8 ==> 6y=8-2x ==> y=-2/6 x + 8/6 ==> y=-1/3x+4/3

x+3y=2 ==> 3y=2-x ==> y=-1/3x +2/3

Both lines have the same slope but different intercepts. They will never intersect.

Be sure you typed the equations correctly.