4'2 Solving Systems of Linear Equations By the Substitution Method

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4.2 Solving Systems of Linear Equations By the
Substitution Method
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Solving Systems of Linear Equations By the
Substitution Method

• The substitution method involves converting the
  system to one equation in one variable by an
  appropriate substitution.

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Steps for Solving Systems of Linear Equations By
the Substitution Method

• Solve either of the equations for one variable in
  terms of the other.
• Substitute the expression from step 1 into the
  other equation.
• Solve the resulting equation.
• Back-substitute the obtained value into the
  equation from step 1.
• Check the solution in both of the original
  equations.

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Solve the System of Linear Equations By the
Substitution Method

• y 2x 8
• 2x 3y 16
• Step 1 Solve either of the equations for one
  variable in terms of the other.
• This has already been done since the first
  equation is already solved for y.

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Solve using substitution y 2x 8 2x
3y 16

• Step 2Substitute the expression from step 1 into
  the other equation.
• 2x 3(2x - 8) 16

Substitute 2x 8 for y
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Solve using substitution y 2x 8 2x
3y 16

• Step 3 Solve the resulting equation.
• 2x 3(2x - 8) 16
• 2x 6x 24 16
• 8x 24 16
• 8x 40
• x 5

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Solve using substitution y 2x 8 2x
3y 16

• Step 4 Back-substitute the obtained value into
  the equation from step 1.
• Substitute x 5 into the first equation.
• y 2(5) 8
• y 10 8
• y 2
• The proposed solution is x 5 and y 2 or the
  ordered pair (5, 2)

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Solve using substitution y 2x 8 2x
3y 16

• Step 5 Check the solution in both equations.
• (5,2)
• Equation 1 Equation 2
• 2 ? 2(5) - 8 2(5) 3(2) ? 16
• 2 ? 10 8 10 6 ? 16
• 2 2 16 16
• True True
• (5, 2) satisfies both equations. The systems
  solution is (5, 2).

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Reference

• Beginning and Intermediate Algebra
• Blitzer
• 2nd Edition