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Systems of Quadratic Equations - Printable Mathematics Worksheets - Wayground

Systems of Quadratic Equations

13 questions

9th - 10th Grade

Mathematics

Systems of Quadratic Equations is a free printable mathematics worksheet for students in Grades 9–10. It contains 13 multiple-choice questions on systems formed by one linear equation and one quadratic equation. Students determine whether a system has zero, one, or two solutions; identify intersection points from graphs; and solve for ordered-pair solutions from given equations. The questions include systems with two intersection points, a single solution, and no solution, helping students connect graphical representations with algebraic results. Students also evaluate candidate coordinate pairs and recognize the possible number of solutions for a linear-quadratic system. The worksheet includes a complete answer key, making it useful for guided practice, independent review, or a quick check of understanding after instruction on solving and interpreting these systems.

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Worksheets

Systems of Quadratic Equations

Total questions: 13

Name
Class
Date
1.

Determine the number of solutions to the given linear-quadratic system.

a)

0 solutions

b)

1 solution

c)

2 solutions

d)

3 solutions

2.

What are the solutions to the graphed system?

a)

(0,-2) and (3,1)

b)

(-2,0) and (2,0)

c)

(0,-2) and (3,1)

d)

(2,2) and (1,0)

3.
a)

A

b)

B

c)

C

d)

D

4.

Solve the system of linear and quadratic equations:

y = 5

y = 2x2 - 16x + 29

a)

(6, 5) and (2, 5)

b)

(2, 6)

c)

(6, 2)

d)

(5, 6) and (5, 2)

5.
Determine the number of solutions to the given linear-quadratic system.
a)
0 solutions
b)
1 solution
c)
2 solutions
d)
3 solutions
6.

What is the solution to the linear-quadratic system graphed in the picture.

a)

(0, 0)

b)

(3, 0)

c)

(2, -3)

d)

(-3, 2)

7.

A system that contains one linear function and one quadratic function can have 0, 1, or 2 solutions.

a)

True

b)

False

c)

Cannot be determined

d)

Nobody cares

8.
Find the solution(s).
a)
(-1,7) and (0,5)
b)
(-4,2) and (-5,8)
c)
(-2,6) and (10,15)
d)
(-2,4) and (6,12)
9.
Two equations were graphed on the set of axes below.  Which point is a solution to the system of equations ?
a)
(0,3)
b)
(5,0)
c)
(2,-3)
d)
(8,9)
10.

What are the solutions to this quadratic/ linear system?

a)

no solution

b)

(3,0) and (4, 5)

c)

(0,3) and (4, -5)

d)

(3,4) and (0,-5)

11.

What are the solutions to this quadratic/ linear system?

a)

(-2, 0) and (3,0)

b)

No Solutions

c)

-6 and -10

d)

(1,-6)

12.
Find the solution(s):
y = x2 - 4x + 6
y = x + 2
a)
(1, 4)
b)
(-1, 1) and (4, 2)
c)
(1, 3) and (4, 6)
d)
(1, 4) and (3, 6)
13.
What are the solutions to the system:
y = x2 + 3x - 5
y = x + 3
a)
(-4, 2) and (-1, 5)
b)
(-4, -1) and (2, 5)
c)
(2, -1 and (-4, 5)
d)
(-4, 1) and (2, -1)
Answer Key

Systems of Quadratic Equations

Total questions: 13

1.
c)

2 solutions

2.
c)

(0,-2) and (3,1)

3.
b)

B

4.
a)

(6, 5) and (2, 5)

5.
c) 2 solutions
6.
c)

(2, -3)

7.
a)

True

8.
d) (-2,4) and (6,12)
9.
d) (8,9)
10.
c)

(0,3) and (4, -5)

11.
b)

No Solutions

12.
c) (1, 3) and (4, 6)
13.
b) (-4, -1) and (2, 5)

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FAQs

What does this Systems of Quadratic Equations worksheet help students learn?

This Grade 9–10 mathematics worksheet helps students solve and interpret systems containing one linear equation and one quadratic equation. Across 13 multiple-choice questions, students determine whether there are zero, one, or two solutions, read intersection points from graphs, and select ordered pairs that satisfy both equations.

How can I use this worksheet to teach linear-quadratic systems?

Introduce the worksheet by reviewing that a system’s solutions are the points shared by its linear and quadratic graphs. Have students first estimate intersections on the graph-based items, then verify coordinate pairs or solve the equation-based systems algebraically. Discuss why some systems have two solutions while others have one or none, using the worksheet’s answer choices to compare possible outcomes.

What mistakes should I watch for when students complete this worksheet?

Students may reverse the coordinates of an intersection, select a point that lies on only one graph, or report an x-value without the corresponding ordered pair. They may also assume every linear-quadratic system has two solutions and overlook the no-solution case. Check that students distinguish among zero, one, and two intersections and verify both coordinates in algebraic solution items.

How do I assign and grade this Systems of Quadratic Equations worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key for the 13 multiple-choice questions. You can assign the PDF for written practice or use the digital version for online responses. Printable submissions can be graded by scanning student work with the Wayground for Teachers app.

How can I differentiate this linear-quadratic systems worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or font size so the coordinate choices, equations, and graph-based questions are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language when helpful for students working through the multiple-choice systems questions.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across all subjects, with downloadable PDFs and answer keys to help students master essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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