Question 41938
Okay, let me show you...the idea of linear combination is to combine equations in such a way (by adding or subtracting them) that eliminates one of the variables...by example...we can add these equations
2X -3Y = -16
X + 3Y = 10
and get
3X = -6
and X = -2
Notice how the 3Y and -3Y cancelled each other out when we added them...
From this X = -2, we plug in to either equation to find Y = 4
Second one...same thing...
3X + Y = -8 
-3X + 4Y = -2
we add them to get
5Y = -10
and Y = -2...plug in and get X = -2 
On the third one we subtract equations because if we added them, nothing would cancel...
2X - Y = 1
-(2X + 5Y = -5)
and get
-6Y = 6 and
Y = -1 and thus X = 0
The last one is a bit more complicated s you have to multiply the bottom equation by two before adding them, so from
-2X + 3Y = 14
X - 4Y = -12
we have
-2X + 3Y = 14
2X - 8Y = -24
and we add giving us
-5Y = -10
Y = 2 and x = -4
I have five kids of my own...I know how you feel...
Buy me a beer next time you see me...