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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.
   Solve the linear system using substitution.
    3x – y = 13
    2x + 2y = -10
   Solve the linear system using substitution.
    -x + 3y = 1
    4x + 6y = 8
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.
Solve the system using combination.
 2x – 6y = 19
-3x + 2y = 10
Solve the system using combination.
 3x + 2y = 6
-6x - 3y = -6
We can multiply
                     both equations by
                     a different number!
Solve the system.
 7x - 12y = -22
-5x + 8y = 14
   Solve the system using combination.
     9x – 5y = -7
    -6x + 4y = 2
   Solve the linear system.
     x – 2y = 3                6x – 10y = 12
    2x – 4y = 7              -15x + 25y = -30

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3.2 Solving Linear Systems Algebraically

  • 1.
  • 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