Basic Steps to Solving Linear Systems by Linear Combinations:
1. Put the equations with like terms in the same columns.
2. Multiply one or both equations on both sides to get new coefficients that are opposites.
3. Add those equations and solve for the remaining variable.
4. Use the value you got in Step 3 in either of the original equations and solve for the other variable.
5. Check your solutions.

The Equations: 2x + y = 5
3x – 2y = 4

Step 1: 2x + y = 5
3x – 2y = 4

Step 2: 3(2x + y = 5) -2(3x – 2y = 4)
6x + 3y = 15 -6x + 4y = -8

Step 3: 6x + 3y = 15
-6x + 4y = -8
0x + 7y = 7
7 7
y = 1

Step 4: 2x + (1) = 5
- 1 - 1
2x = 4
2
x = 2

Now… Try some of these examples on your own…. Check them with your teachers!!! Hopefully you have as great a teacher as our dear, dashing 33 year-old Mr. Ford.

2x + 3y =5
5x + 4y = 16

3x – 2y = 4
4x + 2y = 10

x + y = 8
x – y = 4