We are given two equations as shown above. Call them A and B.
A: 5x + y = 2
B: 4x + y = 5
Both A and B have a y term. If you add the y terms you get 2y, which doesn't help. What does help is to subtract. Another name for the Linear Combination method is the Elimination Method - with the goal to Eliminate one of the variables.
5x + y = 2
4x + y = 5
Now we multiply equation B by -1 so that we can subtract.
5x + y = 2
-4x - y = -5
We add the two new equations together.
1x = -3
So x = -3. Now we take x = -3 and put it back into an original equation. Choose B.
4x + y = 5
4(-3) + y = 5 putting in x = -3
-12 + y = 5 multiplying the -3
y = 17 adding 12 to both sides
Our solution is x = -3, y = 17, or the ordered pair (-3, 17).
