Solving Systems of Equations using Substitution

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Solving Systems of Equations using Substitution
HCPS Henrico County Public Schools Designed by
Vicki Hiner- Godwin High School
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Solving Systems of Equations using Substitution

• Steps
• 1. Solve One equation for One variable.( y
  x a)
• 2. Substitute equation from step one into other
  equation. (Get an equation with only one
  variable.)
• 3. Solve for the first variable.
• 4. Go back and use the found variable in step 3
  to find second variable.
• 5. Check the solution in both equations of the
  system.

WHAT DO WE DO???? CLICK TO SEE AN EXAMPLE
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GIVEN EXAMPLE
y 4x 3xy-21
STEP1 y4x (already solved for y)
STEP 2 Substitute for y in the second equation
3x y -21 and it becomes
3x 4x -21
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GIVEN EXAMPLE
y 4x 3xy-21
STEP 3 Solve for the variable.
3x 4x-21 7x-21 x-3
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GIVEN EXAMPLE
y 4x 3xy-21
STEP 4 Solve for the other variable. Use x-3
and y4x.
y4x and x -3 therefore y4(-3) or y -12
Solution to the system is (-3,-12).
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GIVEN EXAMPLE
y 4x 3xy-21
Check solution. ( -3,-12)
y4x -124(-3) -12-12
3xy-21 3(-3)(-12)-21 -9(-12)-21 -21-21
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Solving Systems of Equations using Substitution

• Steps
• 1. Solve One equation for One variable.( y
  x a)
• 2. Substitute equation from step one into other
  equation. (Get an equation with only one
  variable.)
• 3. Solve for the first variable.
• 4. Go back and use the found variable in step 3
  to find second variable.
• 5. Check the solution in both equations of the
  system.

QUESTIONS?
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GIVEN EXAMPLE
x y10 5x - y2
STEP1 Solve for y. x y 10 y -x 10
STEP 2 Substitute for y in the second
equation 5x - y 2 and it becomes
5x - (-x10) 2
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GIVEN EXAMPLE
x y10 5x - y2
STEP 3 Solve for the variable.
5x-(-x10)2 5xx-102 6x-102 6x12 x2
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GIVEN EXAMPLE
x y10 5x - y2
STEP 4 Solve for the other variable. Use x2 and
xy10.
x2 and xy 10 therefore 2y10 and y 8
Solution to the system is (2,8).
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GIVEN EXAMPLE
x y10 5x - y2
Check solution. (2,8)
5x-y2 5(2)-(8)2 10-82 22
x y10 2810 1010
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THE END OF NOTES! You TRY
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