1. REVIEW: Solving Linear Systems by Elimination
1. Arrange the equations with like terms in columns.
2. If necessary, multiply one or both of the equations by a number to obtain coefficients that are opposites for one of the variables.
3. Add the two equations to eliminate one variable. Solve for the remaining variable.
4. Substitute the value of the known variable into either of the original equations and solve for the other variable.
5. Check the solution in both original equations.

2. Example 1:
Example 2:
Example 3:

3. Multiplication of One Equation
Choose which variable you want to cancel In this case the x looks easier to work with.
1 and 1 (the coefficient of x in both equations) are NOT opposites.
1 and -1 are opposites.
Multiply one of the equations by (-1) turn change 1 to -1.

4. Example 4:
Example 5:

5. Multiplication of Both Equations
Choose which variable you want to cancel.
If you choose x, find the LCM (2, 3):
2, 4, 6, 8, 10, … 3, 6, 9, 12, 15, …
This means you want one equation to have a 6 and the other -6 as the coefficients of x. Multiply the first equation by 3 and the second by -2.

6. Example 6:
Example 7: