Algebra II
Unit 3 Test- Linear Systems and Inequalities Review
Name: _______________________________
Date: _________________
Solve each system by graphing. Then describe each system as consistent and independent, consistent and
dependent, or inconsistent.
Solve the following linear systems by graphing.
2
y   x3
1.
3
2x + 4y = 8
2.
solution:
__________
description:
__________
2x = 10 - 5y
2y = 3x + 4
solution:
___________
description:
___________
Solve the following linear systems by substitution. Then describe each system as consistent and
independent, consistent and dependent, or inconsistent.
3.
-5x + 7y = 19
x = -3y + 5
solution: ___________
description: __________
4.
y = -5x
-3x = 2y + 66
solution: ___________
description: __________
5.
x + 3y = -7
2x + 6y = 1
solution: ___________
description: __________
6.
6x + 15y = -3 solution: ___________
-10x + 10y = -9 description: __________
Solve the following linear systems by elimination. Describe each as consistent and independent, consistent
and dependent, or inconsistent.
7.
5x – 9y = 6
-5x + 2y = -13
solution: ___________
description: __________
8.
4x - 5y = 8
7x – 5y = 41
solution: ___________
description: __________
9.
3x + 2y – 9 = 2
8y – 4x = -4
solution: ___________
description: __________
10.
5x – 8y = 20
solution: ___________
-24y = -15x + 60 description: __________
Solve the following linear systems using any method.
11.
3y = 4x – 12
4x – 5y = 19
13.
solution: ___________
12.
2
x  7y  11
3
3x + 5y = 13
Find the value of two numbers if their sum is 45 and their difference is 7.
solution: ___________
Graph the following linear inequalities.
3
x9
5
14.
y > -2x + 7
15.
y
16.
y<8
17.
x > -6
18.
3x – 2y > 6
19.
x+y>8
Graph the solution to the following systems of inequalities.
20.
y < -2x + 5
y > 5x – 8
21.
3x – y < 4
x > -2
22.
2
y   x5
3
2
y   x8
3
23.
y  2x  7
3
y   5
4
x8
Write the equations to describe each system of inequalities.
24.
25.
Solve the following problem.
26.
The SCA is selling cookie dough and pizza kits for a fundraiser. Shelly sold 10 containers of cookie dough
and 18 pizza kits for $516.50. Andre sold 15 containers of cookie dough and 9 pizza kits for $383.25.
What is the cost of a container of cookie dough and of a pizza kit? Write and solve a system of equations
to justify your answer.