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Alg 2 Test 6: Systems of 2 Equations - Printable Math Worksheets 12th Grade - Wayground

Alg 2 Test 6: Systems of 2 Equations

Alejandro Vargas

Created by Alejandro Vargas

20 questions

12th Grade

Math

Updated Sept 2025

Alg 2 Test 6: Systems of 2 Equations is a Grade 12 mathematics worksheet that assesses how students classify and solve systems of two linear equations. Students determine whether a system has no solution, one solution, or infinitely many solutions; solve systems and record answers as ordered pairs; and identify features of slope-intercept form, including the slope, y-intercept, x-coordinate, and y-coordinate. This 20-question assessment combines 15 multiple-choice questions with fill-in-the-blank items, an equation-labeling drag-and-drop task, a matching item, and an open-ended response. The varied formats give teachers evidence of both procedural fluency and vocabulary understanding, including whether students can distinguish equivalent equations from intersecting or parallel lines. It is a free printable worksheet with a complete answer key, suitable for independent practice, review, or an assessment of systems-of-equations skills.

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Alg 2 Test 6: Systems of 2 Equations

Total questions: 20

Name
Class
Date
1.
This system has _____ solutions
This system has _____ solutions
a)
0
b)
1
c)
2
d)
Infinitely many
2.
When you graph the exact same equation two times,

When you graph the exact same equation two times,

a)
you will have no solution. 
b)
you will have one solution.
c)
you will have infinite solutions. 
d)
you will graph a giraffe. 
3.
Solve the system. Record your answer as (x,y). (Hint: Use Menu32)

Solve the system. Record your answer as (x,y). (Hint: Use Menu32)

(a)  

4.
Solve for x and y.
y = 2/3x - 2
y = -x + 3
a)
(0,3)
b)
(0,-3)
c)
(3,0)
d)
(-3,0)
5.
Solve for x and y
3x + 2y = 16
7x + y = 19
a)
(-2,5)
b)
(-2,-5)
c)
(2,-5)
d)
(2,5)
6.
Solve for x and y
y = 2x + 1
y = 4x - 1
a)
(1,3)
b)
(-1,-3)
c)
(-1,3)
d)
(3,1)
7.
How many solutions will this system have?
How many solutions will this system have? 
a)
No solution
b)
One Solution
c)
I Don't Know
d)
Infinitely Many Solutions
8.
Solve for x and y
3x + 2y = 16
7x + y = 19
a)
(-2,5)
b)
(-2,-5)
c)
(2,-5)
d)
(2,5)
9.

Solve the following systems of equations.

2y + x = -15

x = 3y

a)

(-3, -9)

b)

(-9, -3)

c)

(-3, 9)

d)

(9, -3)

10.
How many solutions will this system have?
How many solutions will this system have?
a)
One
b)
Two
c)
No Solution
d)
Infinitely Many Solutions
11.
How many solutions will this system have?
How many solutions will this system have?
a)
No Solution
b)
Infinitely Many Solutions
c)
No Clue
d)
One solution
12.

Which system of linear equations has no solution?

a)
Which system of linear equations has no solution?
b)
Which system of linear equations has no solution?
c)
Which system of linear equations has no solution?
13.

What is 'b' in this linear equation? y= 5x - 6

a)

6

b)

5

c)

y

d)

-6

14.

Label the following equation with the correct parts.

a)

slope

b)

y-intercept

c)

y-coordinate

d)

x-coordinate

1
2
3
4
1)
2)
3)
4)
15.

What does the "4" represent in the equation y = 4x - 35?

(a)  

16.

What is the y-intercept in the following equation:

y= 25x + 5

a)

25

b)

5

c)

y

d)

x

17.

What is the slope in the following equation:

y = 15x − 3y\ =\ \frac{1}{5}x\ -\ 3

a)

15\frac{1}{5}

b)

-3

c)

3

d)

x

18.

Correctly label the slopes and y-intercepts with their kinds of solutions.

One Solution

Different Slope

Same or Different Y-Int.

No Solution

Same Slope

Different Y-Intercept

Infinite Solutions

Same Slope

Same Y-Intercept

19.

What is the "m" in the equation:

y = 81x - 14

a)

81

b)

14

c)

-14

d)

81x

20.

What are your favorite things to eat at Thanksgiving?

(Write at least 2 complete sentences)

(Ex. My favorite thing to eat at Thanksgiving is _______ because _________)

(Ex. I also like to eat _______ at Thanksgiving because ___________)

(Ex. My family and I love to eat _________ when we get together at Thanksgiving.)

4 lines
WaygroundAnswer Key

Alg 2 Test 6: Systems of 2 Equations

Total questions: 20

1.
a) 0
2.
c) you will have infinite solutions. 
3.
(8,5), (8, 5)
4.
c) (3,0)
5.
d) (2,5)
6.
a) (1,3)
7.
a) No solution
8.
d) (2,5)
9.
b)

(-9, -3)

10.
a) One
11.
b) Infinitely Many Solutions
12.
b)
13.
d)

-6

14.
a
b
c
d
15.
slope
16.
b)

5

17.
a)

15\frac{1}{5}

18.

One Solution

 - 

Different Slope

Same or Different Y-Int.

, 

No Solution

 - 

Same Slope

Different Y-Intercept

, 

Infinite Solutions

 - 

Same Slope

Same Y-Intercept

19.
a)

81

20.
n/a

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FAQs

What does this systems of equations worksheet cover?

This Grade 12 worksheet covers classifying systems as having no solution, one solution, or infinitely many solutions, then solving systems and recording solutions as ordered pairs. Its 20 items use multiple choice, fill-in-the-blank, labeling, matching, and open-ended formats, while also checking students’ understanding of slope-intercept features such as slope and y-intercept.

How can I use this worksheet to teach classifying and solving systems of equations?

Introduce the three solution classifications by connecting them to graphs: parallel lines indicate no solution, intersecting lines indicate one solution, and coincident lines indicate infinitely many solutions. Then use the worksheet’s ordered-pair problems for guided practice, asking students to substitute each coordinate into both equations before moving to the independent multiple-choice and fill-in-the-blank items. Use the labeling task to reinforce the vocabulary of slope-intercept form.

What mistakes should I watch for on this systems of equations worksheet?

Watch for students choosing a solution count without distinguishing parallel lines from identical equations, especially when both equations represent the same line. In the solving items, students may reverse the order of an ordered pair, change a sign, or select coordinates that satisfy only one equation. The equation-labeling and vocabulary items may also reveal confusion between slope, y-intercept, x-coordinate, and y-coordinate.

How do I assign and grade this systems of equations worksheet?

You can assign this worksheet as a printable PDF or as a digital quiz on Wayground. It includes a complete answer key for the multiple-choice, fill-in-the-blank, labeling, matching, and open-ended components. For printable submissions, scan student work with the Wayground for Teachers app to help grade responses efficiently.

How can I differentiate this systems of equations worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or choose a larger font size for the ordered-pair problems, solution-classification questions, and equation-labeling task. You can also enable a dyslexia-friendly font or translate the worksheet into another language, helping students access the mathematical directions and vocabulary without changing the systems-of-equations content.

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

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