Download Solving by substitution notes deciding which variable to solve for

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7.2
Page 137
Solving Linear Systems
by Substitution
Goals p Use substitution to solve a linear system.
p Model a real-life situation using a linear system.
SOLVING A LINEAR SYSTEM BY SUBSTITUTION
Step 1 Solve one of the equations for one of its variables .
Step 2 Substitute the expression from Step 1 into the other
equation and solve for the other variable .
Step 3 Substitute the value from Step 2 into the revised
equation from Step 1 and solve.
Step 4 Check the solution in each of the original equations.
Example 1
Choosing an Equation to Solve
Tell which equation you would use to isolate a variable. Explain your
reasoning.
a. 6x ⫹ y ⫽ ⫺5
2x ⫺ 3y ⫽ 10
Equation 1
Equation 2
b. 5c ⫺ 2d ⫽ 1
c ⫹ 3d ⫽ 0
Equation 1
Equation 2
Solution
a. It would be easiest to isolate y in Equation 1 because the
variable has a coefficient of 1 .
b. It would be easiest to isolate c in Equation 2 because the
variable has a coefficient of 1 .
Lesson 7.2 • Algebra 1 Notetaking Guide
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Mt1nt_07
tran wk bk
7/22/03
2:38 PM
Page 138
The Substitution Method
Example 2
Solve the linear system.
2x 5y 13
Equation 1
x 3y 1
Equation 2
Solution
1. Solve for x in Equation 2 because it is easy to isolate x.
x 3y 1
Revised Equation 2
2. Substitute 3y 1 for x in Equation 1 and solve for y.
2x 5y 13
2( 3y 1 ) 5y 13
6y 2 5y 13
11y 2 13
11y 11
y 1
Write Equation 1.
Substitute for x.
Distribute.
Simplify.
Add 2 to each side.
Solve for y.
3. To find the value of x, substitute 1 for y in the revised
Equation 2 and solve for x.
x 3y 1
Write revised Equation 2.
x 3(1) 1
Substitute for y.
x 4
Simplify.
4. Check that ( 4 , 1 ) is a solution by substituting 4 for
x and 1 for y in each of the original equations.
Equation 1
Equation 2
2x 5y 13
x 3y 1
2( 4 ) 5( 1 ) ⱨ 13
4 3( 1 ) ⱨ 1
8 5 ⱨ 13
4 3 ⱨ 1
13 13
Answer The solution is ( 4 , 1 ).
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Algebra 1 Notetaking Guide • Chapter 7
1 1
Mt1nt_07
tran wk bk
7/22/03
2:38 PM
Page 139
Checkpoint Tell which equation you would use to isolate a
variable. Explain your reasoning.
1. x ⫺ 2y ⫽ 0
2. 4x ⫹ 2y ⫽ 10
x ⫺ 8y ⫽ ⫺5
7x ⫺ y ⫽ 12
I would isolate x in the
first equation because it
is easy to do so and the
value is easy to substitute
in the other equation.
I would isolate y in the
second equation because
it is easier to do so than
to isolate y in the first
equation or x in either
equation.
Use the substitution method to solve the linear system.
3. y ⫽ x ⫺ 1
4. y ⫽ ⫺5x ⫹ 3
x ⫺ 5y ⫽ ⫺15
3x ⫹ 2y ⫽ ⫺8
(5, 4)
(2, ⫺7)
Lesson 7.2 • Algebra 1 Notetaking Guide
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