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Graphing Systems of Nonlinear Equations - Printable Mathematics Worksheets - Wayground

Graphing Systems of Nonlinear Equations

14 questions

10th - 10th Grade

Mathematics

Graphing Systems of Nonlinear Equations is a Grade 10 mathematics worksheet with 14 multiple-choice questions focused on solving and interpreting systems involving nonlinear graphs. Students use Desmos to find intersection points for systems such as a parabola and a line, a parabola and a horizontal line, or two parabolas. They also identify solutions from provided graphs, select a graph that represents a system, and determine whether a given point satisfies both equations. The worksheet reinforces that a system’s solution is an intersection point shared by both equations. Students work with systems that have one solution, multiple solutions, or no solution, and complete a final item using any valid method. This free printable worksheet includes a complete answer key, making it useful for Grade 10 practice, independent work, review, or a quick formative assessment of nonlinear-system reasoning.

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Graphing Systems of Nonlinear Equations

Total questions: 14

Name
Class
Date
1.

Solve by graphing on Desmos:

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)

2.

Solve by graphing on Desmos:

y = x2 - 4x + 6

y = x + 2

a)

(3, 1) and (6, 4)

b)

(-1, 1) and (4, 2)

c)

(1, 3) and (4, 6)

d)

(1, 4) and (3, 6)

3.

Solve by graphing on Desmos:

y = 5

y = 2x2 - 16x + 29

a)

(6, 5) and (2, 5)

b)

(2, 6)

c)

(6, 2)

d)

(5, 6) and (5, 2)

4.

Solve by graphing on Desmos:

y = x2 + 4

y = -x2 - 4

a)

(0, 0) and (0, 4)

b)

(0, 4) and (0, -4)

c)

(4, -4)

d)

No solution

5.

Solve by graphing on Desmos:

y = x2 - 3x

y = -x2 - 3x

a)

(0, 0) and (0, 3)

b)

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

c)

(0, 0)

d)

No solution

6.

Identify the solution to the system graphed here.

a)

(-4, 0) and (1, 0)

b)

(-4, -1)

c)

(-4, 1)

d)

No solution

7.

Identify the solution to the system graphed here.

a)

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

b)

(2, -2)

c)

(0 4)

d)

No solution

8.

Identify the solution to the system graphed here.

a)

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

b)

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

c)

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

d)

No solution

9.
a)
A
b)
B
c)
C
d)
D
10.

Which of the following graphs correctly represents:
y=x2y=x^2  
y=−2x+1y=-2x+1  

a)
b)
c)
d)
11.

 Determine if the point (2, 0) is a solution to the following system:
y=2x−4y=2x-4
y=x2−4y=x^2-4  

a)

Yes, because it works in only one equation.

b)

Yes, because it works in both equations.

c)

No, because it works in neither equation.

d)

No, because it works in only one equation.

12.

Is the point (2, 7) a solution to this nonlinear system?

a)

Yes a solution

b)

No Not a solution

13.

Is the point (5, 3) a solution to this nonlinear system?

a)

Yes a solution

b)

No Not a solution

14.

Solve the System using ANY method:

y = −x2+6x−9y\ =\ -x^2+6x-9  
y = x2−2x−3y\ =\ x^2-2x-3  

a)

(3, 0)

b)

(1, -4)

c)

(3, 0) and (1, -4)

d)

No solution! It is an Inconsistent System

Answer Key

Graphing Systems of Nonlinear Equations

Total questions: 14

1.
b)

(-4, -1) and (2, 5)

2.
c)

(1, 3) and (4, 6)

3.
a)

(6, 5) and (2, 5)

4.
d)

No solution

5.
c)

(0, 0)

6.
c)

(-4, 1)

7.
d)

No solution

8.
a)

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

9.
d) D
10.
b)
11.
b)

Yes, because it works in both equations.

12.
a)

Yes a solution

13.
b)

No Not a solution

14.
c)

(3, 0) and (1, -4)

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FAQs

What does this worksheet cover, and how does it help students solve nonlinear systems?

This Grade 10 worksheet uses 14 multiple-choice questions to practice solving systems of nonlinear equations by graphing, including graphing selected systems in Desmos and reading intersections from provided graphs. Students build the skill of identifying every point shared by both graphs, recognizing one, multiple, or no solutions, and checking whether a given coordinate satisfies both equations.

How can I use this worksheet to teach solving nonlinear systems by graphing?

Introduce the worksheet by modeling how to enter both equations in Desmos and interpret each intersection as an ordered-pair solution. Then have students explain why a point must lie on both graphs, compare the graph-reading items with the point-checking items, and discuss how the systems with no intersection differ from those with one or two intersections.

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

Students may choose a coordinate that lies on only one graph, record an intersection with reversed x- and y-values, or stop after finding one intersection when two are present. They may also select a point near a graph without verifying it in both equations, or mistake separate graphs with no intersection for a solution.

How do I assign and grade this nonlinear systems worksheet?

Wayground provides this worksheet as a printable PDF and as a digital quiz, and it includes a complete answer key for the 14 multiple-choice questions. You can grade printable submissions by scanning student work with the Wayground for Teachers app, or review responses through the digital quiz.

How does this worksheet help students distinguish one solution, multiple solutions, and no solution?

Several items require students to classify systems from their graphs or equations: some have two intersection points, some have one, and at least one has no intersection. This variety helps students connect the number of shared points to the number of solutions rather than treating every nonlinear system as if it must have a single answer.

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 support mastery of essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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