Solving%20Systems%20of%20Equations%20using%20Substitution

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Solving Systems of Equations using Substitution
Ms Murphy Morgan Park High School Chicago
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Lesson Objective

• Solve systems of equations by substitution method.

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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 into second equation 3x
y -21 becomes
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GIVEN EXAMPLE
y 4x 3xy-21
STEP1 y4x (Already solved for y)
STEP 2 Substitute into second equation 3x
y -21 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
Review Steps --Questions?
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.
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GIVEN EXAMPLE
x y10 5x - y2
STEP1 Solve for y x y 10 y -x 10
STEP 2 Substitute into second equation 5x - y
2 becomes
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GIVEN EXAMPLE
x y10 5x - y2
STEP1 Solve for Y x y 10 y -x 10
STEP 2 Substitute into second equation 5x - y
2 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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