Download Study Guide and Intervention Substitution

NAME
6-2
DATE
PERIOD
Study Guide and Intervention
Substitution
Solve by Substitution
One method of solving systems of equations is substitution.
Example 1
Use substitution to
solve the system of equations.
y = 2x
4x - y = -4
Example 2
Solve for one variable,
then substitute.
x + 3y = 7
2x - 4y = -6
Substitute 2x for y in the second
equation.
4x - y = -4
Second equation
4x - 2x = -4
y = 2x
2x = -4
Combine like terms.
x = -2
Divide each side by 2
Solve the first equation for x since the coefficient
of x is 1.
First equation
x + 3y = 7
x + 3y - 3y = 7 - 3y
Subtract 3y from each side.
x = 7 - 3y
Simplify.
Find the value of y by substituting 7 - 3y for x
in the second equation.
2x - 4y = -6
Second equation
2(7 - 3y) - 4y = -6
x = 7 - 3y
14 - 6y - 4y = -6
Distributive Property
14 - 10y = -6
Combine like terms.
14 - 10y - 14 = -6 - 14 Subtract 14 from each side.
-10y = -20
Simplify.
y=2
Divide each side by -10
and simplify.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Use y = 2x to find the value of y.
First equation
y = 2x
y = 2(-2)
x = -2
y = -4
Simplify.
The solution is (-2, -4).
and simplify.
Use y = 2 to find the value of x.
x = 7 - 3y
x = 7 - 3(2)
x=1
The solution is (1, 2).
Exercises
Use substitution to solve each system of equations.
1. y = 4x
3x - y = 1
2. x = 2y
y=x-2
3. x = 2y - 3
x = 2y + 4
4. x - 2y = -1
3y = x + 4
5. x - 4y = 1
2x - 8y = 2
6. x + 2y = 0
3x + 4y = 4
7. 2b = 6a - 14
3a - b = 7
8. x + y = 16
2y = -2x + 2
9. y = -x + 3
2y + 2x = 4
10. x = 2y
0.25x + 0.5y = 10
Chapter 6
11. x - 2y = -5
x + 2y = -1
75
12. -0.2x + y = 0.5
0.4x + y = 1.1
Glencoe Algebra 1
NAME
3-2
DATE
PERIOD
Study Guide and Intervention
Solving Systems of Equations Algebraically
Substitution
To solve a system of linear equations by substitution, first solve for one
variable in terms of the other in one of the equations. Then substitute this expression into
the other equation and simplify.
Example
Use substitution to solve the system of equations.
2x - y = 9
x + 3y = -6
Solve the first equation for y in terms of x.
2x - y = 9
First equation
-y = -2x + 9
Subtract 2x from both sides.
y = 2x - 9
Multiply both sides by -1.
Substitute the expression 2x - 9 for y into the second equation and solve for x.
x + 3y = -6
Second equation
x + 3(2x - 9) = -6
Substitute 2x - 9 for y.
x + 6x - 27 = -6
Distributive Property
7x - 27 = -6
Simplify.
7x = 21
Add 27 to each side.
x=3
Divide each side by 7.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Now, substitute the value 3 for x in either original equation and solve for y.
First equation
2x - y = 9
2(3) - y = 9
Replace x with 3.
6-y=9
Simplify.
-y = 3
Subtract 6 from each side.
y = -3
Multiply each side by -1.
The solution of the system is (3, -3).
Exercises
Solve each system of equations by using substitution.
1. 3x + y = 7
4x + 2y = 16
2. 2x + y = 5
3x - 3y = 3
3. 2x + 3y = -3
x + 2y = 2
4. 2x - y = 7
6x - 3y = 14
5. 4x - 3y = 4
2x + y = -8
6. 5x + y = 6
3-x=0
7. x + 8y = -2
x - 3y = 20
8. 2x - y = -4
4x + y = 1
9. x - y = -2
2x - 3y = 2
10. x - 4y = 4
2x + 12y = 13
11. x + 3y = 2
4x + 12 y = 8
12. 2x + 2y = 4
x - 2y = 0
Chapter 3
31
Glencoe Algebra 2