Linear systems can be solved by multiplying one or both equations by a constant so that adding or subtracting the equations eliminates one variable. The document provides two examples of solving linear systems - one where one equation is multiplied and then added, and another where both equations are multiplied and then subtracted. It also provides practice problems for readers to try solving linear systems on their own.

2. Solve Linear Systems by Multiplying First
Linear System: 5x + 2y = 16
3x – 4y = 20
For systems like these, neither variable can be eliminated by
adding or subtracting
WHAT TO DO: Multiply one or both of the equations by a
nonzero constant so that adding or subtracting the equations
will eliminate one variable.

3. Example 1: Multiply one equation, then add
Solve the Linear System: 3x – 3y = 21 Equation 1
8x + 6y = -14 Equation 2
SOLUTION
STEP 1 Multiply Equation 1
by 2 so that the coefficients
of y are opposites.
STEP 2 Add the equations
STEP 3 Solve for x.
STEP 4 Substitute for x in either of
the original equations and solve for y.

4. Example 2: Multiply both equations, then subtract
Solve the Linear System: 4x + 5y = 35 Equation 1
2y = 3x - 9 Equation 2
SOLUTION
STEP 1 Arrange the equations
so that like terms are in columns.
STEP 2 Multiply Equation 1 by 2
and Equation 2 by 5
STEP 3 Subtract the equations.
STEP 4 Solve for x.
STEP 5 Substitute for x in either of
the original equations and solve for y.

5. Try on your own:
1. 4x – y = 9 2. 4x – 3y = 8
5x + 2y = 21 5x – 2y = -11

6. Textbook p. 401 – 403 # 3 – 13 odd
17 – 27 odd
33 – 38 all