Unit 6 End of Unit Review
Name________________________________________
1. a. What does it mean for an ordered pair to be a solution to a system of equations?
b. Is x = 4, y = 7 a solution to the system of equations shown? Justify your answer.
2 𝑥 − 6 𝑦 = 12
{
3𝑥 + 4𝑦 = 40
2. At Pottsgrove High School, there are a total of 515 students in the freshman and sophomore classes
combined. The freshman class has 9 more students than the sophomore class. Which system of
equations could be used to determine the number of freshmen (f) and sophomores (s) in the school?
𝑓 + 𝑠 = 515
a. {
𝑠 =𝑓+9
𝑓 − 𝑠 = 515
b. {
𝑠 =𝑓+9
𝑓 + 𝑠 = 515
c. {
𝑓 =𝑠+9
𝑓 − 𝑠 = 515
d. {
𝑓 =𝑠+9
3. a. Which system of equations is graphed here?
4
3
𝑦 = 𝑥−4
i) {
1
𝑦 = −2𝑥 + 7
4
𝑦 = 3𝑥 + 4
iii) {
1
𝑦 = − 𝑥−7
2
ii) {
𝑦 =𝑥−4
𝑦 = −𝑥 + 7
3
𝑦 = 4𝑥 − 4
iv) {
𝑦 = −2𝑥 + 7
b. What is the solution to the system of equations
graphed?
𝑦 = 3𝑥 − 2
4. Masai solves the system of equations {
using the tables shown.
𝑦 = −2𝑥 + 3
x
-1
0
1
2
y = 3x - 2
-5
-2
1
4
x
-1
0
1
2
y = -2x + 3
5
3
1
-1
a. Explain how the tables can be used to find the solution to the system.
b. What is the solution to this system of equations?
5. Kayla is solving systems of equations algebraically. She can do the algebra, but she does not know
what the results mean. Describe what each result means and what the graph would look like.
a. Result of x = 4, y = −1.
What does this result mean? Circle one: One solution /No solution /Infinitely many solutions
What do you know about the graph for this system of equations?
b. Result of 3 = 5.
What does this result mean? Circle one: One solution /No solution /Infinitely many solutions
What do you know about the graph for this system of equations?
c. Result of 8 = 8.
What does this result mean? Circle one: One solution /No solution /Infinitely many solutions
What do you know about the graph for this system of equations?
6. Solve using the substitution method. Report the solution and check that it is correct.
𝑥 − 2𝑦 = 1
{
5𝑥 − 3𝑦 = 19
7. Solve using the linear combination method. Report the solution and check that it is correct.
2𝑥 + 3𝑦 = 36
{
−4𝑥 − 6𝑦 = 12
8. Apply all steps from the routine for solving linear systems of equations for the following problem.
Honey Flakes Cereal puts tokens in its cereal boxes. The tokens are either gold or silver. Gold tokens
are worth 8 points and silver tokens are worth 4 points. If Marcus has collected 11 tokens and the
total value for those tokens is 64 points, determine the number of each type of token Marcus has.