This document provides examples of solving systems of linear equations using substitution and combination methods. It demonstrates solving 3x+4y=-4 and x+2y=2 by substitution, solving -x+3y=1 and 4x+6y=8 by substitution, and solving 2x-4y=13 and 4x-5y=8 by combination. It also shows multiplying equations by constants before combining, and solving a 4 equation system.

2. Example:  1. Solve one equation
for one variable.
3x + 4y = -4
x + 2y = 2  2. Substitute that into
the other equation and
solve.
 3. Plug in that answer
and solve for the other
variable.

3.  Solve the linear system using substitution.
3x – y = 13
2x + 2y = -10

4.  Solve the linear system using substitution.
-x + 3y = 1
4x + 6y = 8

5. Example:  1. Multiply one or
both equations by a
2x – 4y = 13 constant.
4x – 5y = 8  2. Add the two
equations to eliminate
a variable. Solve for
the other.
 3. Plug in that
solution to solve for
the other variable.

6. Solve the system using combination.
2x – 6y = 19
-3x + 2y = 10

7. Solve the system using combination.
3x + 2y = 6
-6x - 3y = -6

8. We can multiply
both equations by
a different number!
Solve the system.
7x - 12y = -22
-5x + 8y = 14

9.  Solve the system using combination.
9x – 5y = -7
-6x + 4y = 2

10.  Solve the linear system.
x – 2y = 3 6x – 10y = 12
2x – 4y = 7 -15x + 25y = -30