3-2: Solving Systems of Equations using Substitution

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3-2 Solving Systems of Equations using
Substitution
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Solving Systems of Equations using Substitution
Steps 1. Solve one equation for one
variable (y x a) 2. Substitute the
expression from step one into the other
equation. 3. Simplify and solve the
equation. 4. Substitute back into either
original equation to find the value of the
other variable. 5. Check the solution in both
equations of the system.
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Example 1
y 4x 3x y -21
Step 1 Solve one equation for one variable.
y 4x (This equation is already solved
for y.)
Step 2 Substitute the expression from step one
into the other equation. 3x y
-21 3x 4x -21
Step 3 Simplify and solve the equation.
7x -21 x -3
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y 4x 3x y -21
Step 4 Substitute back into either original
equation to find the value of the
other variable. 3x y
-21 3(-3) y -21 -9 y
-21 y -12
Solution to the system is (-3, -12).
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y 4x 3x y -21
Step 5 Check the solution in both equations.
Solution to the system is (-3,-12).
3x y -21 3(-3) (-12) -21 -9
(-12) -21 -21 -21
y 4x -12 4(-3) -12 -12
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Example 2
x y 10 5x y 2
Step 1 Solve one equation for one variable.
x y 10 y
-x 10
Step 2 Substitute the expression from step one
into the other equation. 5x - y 2
5x -(-x 10) 2
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x y 10 5x y 2
Step 3 Simplify and solve the equation.
5x -(-x 10) 2 5x x -10 2 6x
-10 2 6x 12 x
2
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x y 10 5x y 2
Step 4 Substitute back into either original
equation to find the value of the
other variable. x y 10 2
y 10 y 8
Solution to the system is (2,8).
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x y 10 5x y 2
Step 5 Check the solution in both equations.
Solution to the system is (2, 8).
5x y 2 5(2) - (8) 2 10 8 2 2 2
x y 10 2 8 10 10 10
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Solve by substitution
1. 2.