Lesson 5.1 • Solving Systems of Equations
Name
Period
Date
1. Verify whether or not the given ordered pair is a solution to the system.
If it is not a solution, explain why not.
a. (4, 3)
b. (4, 0)
y 0.5x 2
4
y 3x 2
y 0.5x 1
y 0.6x 0.6
d. (3, 2)
c. (5, 3)
e. (3.5, 1.5)
y 5x 13
7
y 3x 9
y 0.75x 0.75
2
1
y 3x 3
f.
12, 23
2
y 4x 23
y 2.5x 7.25
y 2.5x 10.25
5
y 6x 3
2. Graph each system using the window [9.4, 9.4, 1, 6.2, 6.2, 1]. Use the
trace function to find the point of intersection.
y 3x 3
a.
y 3x 9
d.
1
y 2x 3.5
y 3x 11
y 2.5x 4
g.
y 5x 9
y x 4
b.
2
y 3x 3
e.
h.
3
y 4x 4
yx5
3
y 2x 3
y 3x 15
c.
2
yy 2x
1.5x 2.5
f.
yy 2x3x5 15
i.
5
yy 6x
4x 5
3. Use the calculator table function to find the solution to each system of
equations. (You’ll need to solve some of the equations for y first.)
34
a.
5
yy 4x
3x 9
b.
6
yy x2x
c.
3x2x 2yy 54
d.
e.
y2x3x3y82
f.
6
yy 3x
4x 8
2
y 3x 6
y 3x 16
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Lesson 5.2 • Solving Systems of Equations Using Substitution
Name
Period
Date
1. Verify whether or not the given ordered pair is a solution to the system.
If it is not a solution, explain why not.
b. (2, 6)
a. (4, 8)
yy 2x4x 12
3.5x 2.5y 8
1.5x
3.5y 22
c. (2, 1)
d. (3, 2)
0.5
yy 0.75x
1.5x 5
2xx 3y5y34
2. Solve each equation by symbolic manipulation.
a. 7 5x 28 2x
b. 3x 9 x 1
c. 5 2y 3y 2
3. Substitute 2 5x for y to rewrite each expression in terms of one
variable. Combine like terms.
a. 3x y
b. 2y 10x
c. 4x 3y
4. Solve each system of equations using the substitution method, and check
your solutions.
a.
3
yy 2x
1.5x 0.5
b.
3xx 5y11y 2 2
c.
yy 6x3x3 6
d.
x2x2y3y721
e.
yy 4x2x3 9
f.
4xy 2x3y31
g.
xx yy 612
h.
3x2x y5y118
i.
y7x7x3y13
5. Frank’s Specialty Coffees makes a house blend from two types of coffee
beans, one selling for $9.05 per pound, and the other selling for $6.25 per
pound. His house blend sells for $7.37 per pound. If he is using 9 lb of
the $6.25/lb beans, how many pounds of the $9.05/lb beans does he need
to make his house blend?
©2007 Key Curriculum Press
Discovering Algebra More Practice Your Skills
35
Lesson 5.3 • Solving Systems of Equations Using Elimination
Name
Period
Date
1. Use the equation 6x 4y 8 to find the missing coordinate of
each point.
a. (6, y)
b. (3, y)
c. (x, 2)
d. (x, 12.5)
2. Use the equation 2x 3y 0 to find the missing coordinate of
each point.
a. (5, y)
b. (5, y)
1
3
d. x, 5
c. (x, 3)
3. Solve each system of equations by elimination. Show your work.
a.
xx yy 2
0
b.
5x3y 3x4y 143
c.
x2x2y3y45
d.
2x4x 5y5y 1
7
e.
2x3x 6y18y1630
f.
2xy x10 2y
g.
3x2y x3y1018
h.
3x3y 2x4y 2
1
i.
2x4x 6y3y 1
3
j.
3x7x 2y2y 218
k.
2x5x 7y4y 36
l.
5x4x 3y3y 414
m.
3x2x 3y4y 6
14
n.
2y2x 3x2y 6
4
o.
3x5x 5y3y 113
4. Given the system
4x15y6y10x 1025 0
a. Solve the system by elimination.
b. Explain your answer to 4a.
5. Given the system
3x9x2y6y9 12
a. Solve the system by elimination.
b. Explain your answer to 5a.
36
Discovering Algebra More Practice Your Skills
©2007 Key Curriculum Press