Mark the two equations below as A and B,
A: 3x+y=4
B: 2x+y=7
Because there's a y for both A and B, elimination (or linear combination, depending on the book) works well. If we add both equations we get 2y for the y terms. What if we subtracted instead. y - y = 0, and we eliminate the y terms. For subtracting, we multiply B by -1.
3x + y = 4
-2x - y = -7
Adding both equations (remember to change the signs on B) gives that 1x = -3 and so x = -3.
Now we take x = -3 and put into an original equation. Let's go into A.
3x+y=4
3 * -3 + y = 4 letting x = -3
-9 + y = 4
y = 13 adding 9 on both sides
So x = -3 and y = 13, or the ordered pair (-3, 13) - the 2nd one given - is our solution.
