Solving By Substitution

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Solving By Substitution
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• Linear systems can be solved algebraically.
• One way is to use substitution.
• This is easiest when one or both equations is
  given in terms of either x or y.
• This means that the x or y is alone on one side
  of the equal sign.

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Examples

• Both equations given in terms of y
• y 3x 2 y -4x - 7
• One in terms of y, one in terms of x
• y x 5 x 3y - 2
• One equation in terms of y
• y 2x 3y x - 1
• One equation in terms of x
• x 3y -2x y - 3

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Solving With Substitution

• Solve the linear system
• y 2x 1
• y 3x - 2

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Step 1

• Substitute the value of y in equation 1 into
  equation 2.
• y 3x 2 ? equation 2
• y 2x 1 ?equation 1

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Step 1

• Substitute the value of y in equation 1 into
  equation 2.
• 2x 1 3x 2

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Step 2

• Solve for x 2x 1 3x - 2
• Subtract 2x from both sides.
• 2x 2x 1 3x 2x 2
• 1 x 2
• Add 2 to both sides ..
• 1 2 x 2 2
• 3 x

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Step 3

• Substitute the value of x we just found into
  either equation 1 or 2
• y 2x 1
• y 2(3) 1
• y 6 1
• y 7

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Final Answer

• Write the final answer as a coordinate point.
• So, we found our answer to be
• x 3 and y 7.
• So our solution is (3, 7)

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Remember

• The solution to a linear system is the point of
  intersection of two equations.
• That is where the two lines cross and share the
  same value for x and y.