Systems of Equations Quiz
Questions: 16 · 10 minutes
1. A rectangle has a perimeter of 26 units, and its length is 3 units greater than its width. What are its dimensions?
Length 10 units and width 3 units
Length 8 units and width 5 units
Length 7 units and width 6 units
Length 13 units and width 10 units
2. Two notebooks and three pens cost $13. One notebook and one pen cost $5. What is the price of one pen?
$3
$2
$4
$5
3. While eliminating a variable from 2x + 3y = 12 and 2x − y = 4, a student subtracts the second equation from the first and obtains 4y = 8. What should the student conclude?
y = 8, followed by x = 6
y = 2, followed by x = 5
y = 2, followed by x = 3
y = −2, followed by x = 1
4. Classify the system 3x − 6y = 9 and x − 2y = 3.
One solution, because the x-coefficients differ
No solution, because one equation has larger coefficients
Two solutions, because either equation can be solved first
Infinitely many solutions, because the first equation is three times the second
5. Which system has no solution?
x + y = 5 and x − y = 1
y = 2x + 1 and y = −2x + 1
2x + y = 5 and 4x + 2y = 10
2x + y = 5 and 4x + 2y = 12
6. Which ordered pair solves both 3x + y = 8 and x − y = 0?
(3, −1)
(1, 1)
(2, 2)
(1, 5)
7. How many solutions does the system y = 2x + 1 and 2y = 4x + 2 have?
No solutions, because the coefficients are different
Infinitely many solutions, because the equations describe the same line
Exactly one solution, at (0, 1)
Exactly two solutions, because there are two equations
8. Use substitution to solve x = y + 2 and 2x + y = 10.
(4, 2)
(2, 4)
(5, 0)
(3, 2)
9. A student solves y = 2x + 1 and y = 2x − 5 by setting the expressions equal. The work simplifies to 1 = −5. What does this contradiction show?
The value of x is 1
The equations have infinitely many solutions
The system has no solution
The equations must intersect when y = −5
10. Solve the system x + y = 7 and x − y = 1.
(3, 4)
(6, 1)
(4, 3)
(7, 1)
11. What does a solution to a system of two equations represent?
The point where either equation crosses the y-axis
Any value that makes at least one equation true
The slope shared by the two equations
An ordered pair that makes both equations true
12. Two numbers have a sum of 18. If x is the larger number and y is the smaller number, the larger number is 4 more than the smaller. Which statement correctly models these facts?
Their difference is 18, and their sum is 4
Their sum is 18, and the larger number minus the smaller number is 4
Their sum is 18, and the smaller number minus the larger number is 4
Their product is 18, and the larger number divided by the smaller number is 4
13. For the system 2x + 3y = 7 and x − 3y = 5, which first operation most directly eliminates y?
Subtract the second equation from the first
Add the two equations
Multiply only the first equation by 2
Divide both equations by 3
14. On a graph, two nonparallel lines intersect at (−2, 5). What does this point mean for the corresponding system?
The ordered pair (−2, 5) satisfies both equations
Only y = 5 satisfies both equations
Each equation has a different solution
Only x = −2 satisfies both equations
15. At an event, 20 adult and child tickets are sold. Adult tickets cost $12 and child tickets cost $7, producing $190 in total revenue. If x is the number of adult tickets and y is the number of child tickets, which system models the situation?
x + y = 190 and 12x + 7y = 20
x + y = 20 and 7x + 12y = 190
12x + 7y = 20 and x − y = 190
x + y = 20 and 12x + 7y = 190
16. The equations y = −3x + 4 and y = −3x − 2 are graphed on the same coordinate plane. What can you conclude?
They are parallel and the system has no solution
They intersect on the x-axis
They describe the same line
They intersect at (0, 4)