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Systems of Equations Questions - All Grades

You can create printable tests and worksheets from these Systems of Equations questions! Select one or more questions using the checkboxes above each question. Then click the add selected questions to a test button before moving to another page.

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Grade 10 Systems of Equations CCSS: HSA-REI.C.6

Select the solution to the system of linear equations.

$x-7y=23$

$4x-3y=42$

(9, 2)
(4, 3)
(9, -2)
(-7, 3)

Grade 10 Systems of Equations CCSS: HSA-REI.C.6

Select the solution to the system of linear equations.

$x+y=10$

$x-y=4$

(5, 1)
(7, 3)
(-5, -2)
(-7, 3)

Grade 9 Systems of Equations CCSS: HSA-REI.C.6

Solve the system of equations by the SUBSTITUTION method.

$x + 3y = 1$

$−3x − 3y = −15$

(7, −2)
(4, −5)
(3, −1)
(9 −8)

Grade 10 Systems of Equations CCSS: HSA-REI.C.6

Select the solution to the system of linear equations.

$y=-2x-4$

$y=1/2x+1$

(0, 0)
(-2, 0)
$(-1/2, 1/2)$
No Solution

Grade 8 Systems of Equations CCSS: 8.EE.C.8, 8.EE.C.8b

Solve the following system of equations using the substitution method.
x + 2y = 11
3x − 2y = 9

(1, 3)
(2, 7)
(5, 3)
(3, 5)

Grade 9 Systems of Equations CCSS: HSA-REI.C.6

Which system of equations has no solutions?

$a - b = 2, \ \ \ b = -a - 3$
$a-b=3, \ \ \ a+b=-2$
$-a+b=-2, \ \ \ b=a+3$
$a+b=3, \ \ \ -a+b=2$

Grade 9 Systems of Equations CCSS: HSA-REI.C.6

Solving Systems of Equations by ELIMINATION Method.

$x − y = 11$

$2x + y = 19$

(-8, −1)
(10, −1)
(11, −9)
(6, 3)

Grade 8 Systems of Equations CCSS: 8.EE.C.8, 8.EE.C.8c

Mrs. Page needed two types of paper for her art class. The premium color paper costs $40 per case and the plain white paper costs $30 per case. If she bought 20 cases all together and spent $720 total, how many cases of plain white paper did she buy?

4
5
7
9
none of these are correct

Grade 10 Systems of Equations CCSS: HSA-REI.C.6

Select the solution to the system of linear equations.

$x+2y=11$

$3x-2y=9$

$(3, 2)$
$(5, 3)$
$(4.5, 2)$
$(1/2, 2/3)$

Grade 9 Systems of Equations CCSS: HSA-REI.C.6

2x + 9y = 0
3x + 5y = 17

(-9, 2)
(-9, -0)
(9, -2)
(-2, 9)

Grade 10 Systems of Equations CCSS: HSA-REI.C.6

3x - 2y = 7
x + 3y = 6

x = 3, y = 1
x = -1, y = 1.67
x = 0, y = 1
x = 3, y = -2

Grade 10 Systems of Equations

There are 500 black and purple cell phones in a box. The black ones are $200.00 and the purple ones are $250 . The box costs $150,000.00. Use the system of linear equations below to fill in the blanks.

x - Black Cell Phones, y - Purple Cell Phones

x + y = 500
200x + 250y = 150000

Grade 10 Systems of Equations CCSS: HSA-REI.C.6

Solve this system of equations.

$4x - 2y =8$

$-5x + 3y = 9$

$x = 12, y = 15$
$x = 21, y = 38$
$x = 9, y = 8$
$x = -12, y = -15$

Grade 9 Systems of Equations CCSS: HSA-REI.C.6

At what point do the lines

$y = 4x -10$ and

$y = 7x + 11$ intersect?

(-7, -38)
(-5, -10)
(-3, -10)
(-1, 4)

Grade 10 Systems of Equations CCSS: HSA-REI.C.6

What is the value of y in the system of equations:

$x-2y=3$ and

$-x+y=7$ ?

Grade 10 Systems of Equations CCSS: HSA-REI.C.6

Solve the system of equations.
x - y = 6
3x + 2y = -22

(-2, -8)
(6.8, 0.8)
(2, 8)
(-8,-2)

Grade 8 Systems of Equations CCSS: 8.EE.C.8, 8.EE.C.8b

What solution for x and y satisfies the system of equations?
5x + 2y = 41
3x + 2y = 27

(8,1.5)
(-1,15)
(7,3)
(-4,30)

Grade 10 Systems of Equations CCSS: HSA-REI.C.5

For the given system of equations, the following work was done to create another system of equations with the same solution. Is this work correct? If not, choose the correct reason why.

We start with our given system of equations.

$4x-3y=8$

$2x+6y=-11$

We will multiply the first equation by 2. Now we can add this with the second equation.

$ul{:(,4x-6y=,8),(+,2x+6y=,-11):}$

${:( \ \ \ ,6x \ \ \ \ \ \ \ \ \ =, -3):}$

This results in the following new system of equations.

$4x-3y=8$

$6x=-3$

This is correct.
The first equation has to be multiplied by $1/2$ .
The equations should be subtracted.
Only the second term of the first equation was multiplied by 2.

Grade 9 Systems of Equations

Which of the following is NOT a method for solving systems of linear equations?

Solve by graphing.
Solve by substitution.
Solve by elimination.
Solve by contribution.

Grade 10 Systems of Equations CCSS: HSA-REI.C.6

Solve the system of equations.

$4b-2d=5$

$-2b+d=1$

$"Infinite Solutions"$
$(0,1)$
$(1,0)$
$"No Solution"$

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