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
