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Unit 11 Practice Test
Name_______________________________
Per ______
1. How many solutions do the following types of lines have?
a. Parallel: _________________________________
b. Intersecting: _____________________________
c. Coincidental: ______________________________
2. Consider the following system of equations. sider t 3A. Consider the following system of equations.
𝑦 = 5𝑥 − 1
𝑦 = 2𝑥 − 1
𝑦 = 𝑥+3
𝑦 = 2𝑥 + 3
a. Identify the slope and y-intercept of the graph of
each equation.
a. Identify the slope and y-intercept of the graph of
each equation.
b. Based on your answer for part (a), are the graphs
of the two lines intersecting lines, the same
line, or parallel lines? Explain.
b. Based on your answer for part (a), are the graphs
of the two lines intersecting lines, the same
line, or parallel lines? Explain.
c. How many solutions does the system have? Explain
how you can tell without solving the system.
c. How many solutions does the system have? Explain
how you can tell without solving the system.
d. Solve the system by graphing.
d. Solve the system by graphing.
Determine whether the system of equations has one solution, no solution or infinitely many solutions.
2
3
3. 𝑦 = − 𝑥 + 1
𝑦=
1
𝑥
3
+4
5. 4𝑥 + 𝑦 = −3
4𝑥 + 𝑦 = −2
4. 𝑥 − 3𝑦 = −18
−2𝑥 + 6𝑦 = 36
6.
1
3
𝑦 =− 𝑥+2
1
3
𝑦= − 𝑥−2
Solve the system of equations by graphing. Check your answers!
3
7.
𝑦 = 2𝑥 − 2
8.
1
𝑦 = 4𝑥 + 3
3
9.
𝑦 = 𝑥+3
2
1
𝑦 = 2𝑥 − 1
10.
𝑦 =𝑥−2
3𝑥 + 𝑦 = 6
𝑥−𝑦=2
𝑦 = −𝑥
.
Is the ordered pair a solution to the system of equations? Show your work!
11. (4,5);
𝑦 = 𝑥+1
𝑦 = −𝑥 + 5
12. (4, 1);
5𝑥 − 4𝑦 = 16
𝑥 + 4𝑦 = 8
13. (-3, -2);
𝑥 + 3𝑦 = −9
5𝑥 − 3𝑦 = −9
Determine the point of intersection and the break-even point for each graph. Then, state the least
number of items that must be sold in order to make a profit.
14. Point of intersection:
Break-even point:
At least _____ computer mouse pads must be sold to make a profit.
Solve the system using the substitution method.
15.
4𝑥 − 7𝑦 = −17
𝑦 = 3𝑥
16.
𝑥 − 4𝑦 = −24
𝑥 = −𝑦 + 1
Solve the system using the elimination method.
17.
3𝑥 − 4𝑦 = −8
𝑥 + 4𝑦 = −8
18.
𝑥 + 𝑦 = −4
𝑥−𝑦 =2
19. .Look at the following systems and decide the best method (Graphing, Substitution or Elimination) to solve them
and state why.
a.
−7𝑥 − 3𝑦 = 9
Method: __________________ Why?___________________________________________
𝑥 + 3𝑦 = 9
b. 𝑦 = −
𝑦=
c.
1
2
5
𝑥
2
𝑥−4
+2
4𝑥 + 𝑦 = 3
𝑥 =𝑦+5
Method: __________________ Why?__________________________________________
Method: __________________ Why?___________________________________________
Write 2 equations that represent the problem. Next, solve the system of equations (Break-even point) and explain
how many items need to be sold to make a profit.
20. The cost for the marching band to run a car wash as a fundraiser is $10 to use the parking lot and $2 per
car. The marching band plans to charge $5 per car.
a. Equations:
b. Solve (Break-Even Point):
c. How many shirts need to be
sold to make a profit?
Write a system of equations to represent the situation, then solve it using the method of your choice.
21. The sum of two numbers is 103. The larger number is three times the smaller number plus 7. What are
the numbers?
22. Jenny solved a system of equations and got this for the answer: 2 = -5. What does this tell her about
the solution for the system of equations?
UNIT 11 Honor Practice Test Questions
Name_______________________________
Per ______
1. (1 pt) Write the equations of 2 lines that are parallel.
2. (1 pt) Write the equations of 2 lines that are coincidental.
3. (1 pt) Write the equations of 2 intersecting lines.
4. (1 pt) Convince me that (-1, 2) is or is not a solution to the following system.
5
−1 = 16 𝑥 − 12
𝑦
5 = 3𝑥 + 4𝑦
5. (2 pts) Solve the following system:
𝑥− 𝑦=3
−4𝑥 + 7𝑦 = −14
6. (1 pt) Write an equation that shows the relationship between profit, cost, and income.
7. (1 pt) What is the first step in solving this system
2𝑥 − 𝑦 = 11
by the substitution method?
−4𝑥 + 5𝑦 = −9
8. (2 pts) The senior classes at High School A and High School B planned separate trips to the county fair. The
senior class at High School A rented and filled 5 vans and 4 buses with 315 students. High School B rented
and filled 6 vans and 8 buses with 570 students. Every van had the same number of students in it as did the
buses. How many students can a van carry? How many students can a bus carry?