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graphing systems - Printable Mathematics Worksheets - Wayground

graphing systems

13 questions

9th - 9th Grade

Mathematics

This free Grade 9 mathematics worksheet gives students 13 multiple-choice questions on solving systems of linear equations by graphing. Students identify the ordered-pair solution where two lines intersect, determine whether a system has one, no, or infinitely many solutions, and connect each outcome to the relationship between the lines: intersecting, parallel, or identical. The worksheet also includes a point-verification question that asks students to determine whether a given coordinate satisfies both equations. Use the worksheet for guided practice, independent work, or a quick check of students’ understanding after instruction on graphing systems. The repeated solution formats help students connect graphical intersections with algebraic meaning while practicing accurate reading and recording of ordered pairs. It is available as a free printable worksheet and includes a complete answer key for efficient review and grading.

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Worksheets

graphing systems

Total questions: 13

Name
Class
Date
1.
Solve by graphing.
y = 2x + 1
y = 4x - 1
a)
(1,3)
b)
(-1,-3)
c)
(-1,3)
d)
(3,1)
2.

Solve this system of equations by graphing.

y = 1/2x + 2

y = -3x + 9

a)

(2, 3)

b)

(-2, -3)

c)

(3, 2)

d)

(-3, 2)

3.
What is the solution to this system?
a)
(1, -1)
b)
(-1, 1)
c)
(0, -2)
d)
(2, 0)
4.
When you graph the exact same equation twice,
a)
you will have no solution. 
b)
you will have one solution.
c)
you will have infinite solutions. 
d)
you will graph a giraffe. 
5.
How many solutions will this system have? 
a)
No solution
b)
One Solution
c)
I Don't Know
d)
Infinitely Many Solutions
6.
If a system of linear equations has one solution, what does this mean about the two lines? 
a)
Parallel lines
b)
the same line 
c)
Intersecting lines
7.
If a system of linear equations has infinitely many solutions, what does this mean about the two lines? 
a)
Intersecting lines
b)
Same line
c)
Parallel lines
8.
Solve the system by graphing:
y = 6x - 4
y = -x + 3
a)
(1, 2)
b)
(2, 1)
c)
(4, 5)
d)
(2, 4)
9.
What is the solution to the system?
a)
(3, -1)
b)
(2, -6)
c)
No Solution 
d)
(6, -2)
10.
Buzz graphed two lines in order to find the solution to a given system of equations.
What is the solution?
a)
(-1, 4)
b)
(1, -4)
c)
(-4, 1)
d)
(4, -1)
11.
Steffen graphed two lines in order to find the solution to a given system of equations.
What is the solution?
a)
(-3,-8)
b)
(-8,-3)
c)
(3,-8)
d)
(8,3)
12.
These two lines intersect at _____.
a)
(4, -2)
b)
(4, 2)
c)
(-2, 4) 
d)
No solution
13.
Determine if (4, 1) is a solution for the system of equations.
y = -x + 5
y = 2x - 7
a)
yes
b)
no
Answer Key

graphing systems

Total questions: 13

1.
a) (1,3)
2.
a)

(2, 3)

3.
a) (1, -1)
4.
c) you will have infinite solutions. 
5.
a) No solution
6.
c) Intersecting lines
7.
b) Same line
8.
a) (1, 2)
9.
d) (6, -2)
10.
b) (1, -4)
11.
a) (-3,-8)
12.
a) (4, -2)
13.
a) yes

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FAQs

What does this worksheet cover, and how does it help students learn to solve systems by graphing?

This Grade 9 worksheet contains 13 multiple-choice questions on solving systems of linear equations by graphing. Students practice identifying the ordered pair where two lines intersect, recognizing no solution and infinitely many solutions from parallel or identical lines, and checking whether a coordinate satisfies both equations. These tasks connect the visual relationship between lines to the meaning of a system’s solution.

How can I use this worksheet to teach solving systems of linear equations by graphing?

Begin by modeling how to graph both equations and read the intersection as an ordered pair. Then use the worksheet’s questions about identical, parallel, and intersecting lines to have students explain why a system has infinitely many, no, or one solution. Finish with the point-verification item, asking students to substitute the given coordinate into both equations and justify the answer.

What mistakes should I watch for when students complete this systems-by-graphing worksheet?

Watch for students reversing the coordinates of an intersection, selecting a nearby answer choice, or reporting a point that lies on only one line. Students may also confuse parallel lines with identical lines, leading them to choose infinitely many solutions instead of no solution, or overlook that a candidate point must satisfy both equations. For the final verification item, check that they test the coordinate in each equation rather than only one.

How do I assign and grade this graphing systems worksheet?

This worksheet is available as a printable PDF and as a digital quiz on Wayground, so you can assign the format that fits your lesson. It includes a complete answer key for the 13 multiple-choice items, and printable student work can be graded by scanning it with the Wayground for Teachers app. The printable option can also support instruction when your school is reducing screen time.

How can I differentiate this worksheet for students who need support with graphing systems?

Use the worksheet’s Advanced Settings to adjust font spacing or increase the font size, making the system-solving prompts and answer choices easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language when those options support access to the graphing and coordinate questions.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across 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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