Solving systems of equations worksheets

Solving systems of equations worksheets are available on this page. Find out below how you can download and print this worksheet about solving systems of linear equations.

Name: ______________________

Date: __________________________

Find the solution for each system below by elimination or by substitution.

1.
y = 2x - 3
y = x - 1

x = ________   y = ___________

2.
y  =  -2x + 1
y = 2x - 3

x = ________   y = ___________



3.
4x - 2y = 8
2x + 2y = 4

x = ________   y = ___________

4.
-2x - y = -2
2x + 4y = 11

x = ________   y = ___________



5.
6x + 2y = 10
3x + 3y = -13

x = ________   y = ___________

6.
7x - 12y = -13
5x + 4y = 19

x = ________   y = ___________



7.
4x + 2y = 14
7x - 3y = -8

x = ________   y = ___________

8.
15x + 3y = 9
10x + 7y = -4

x = ________   y = ___________





Name: _______________________

Date : _______________________

Tell whether the system below has 1 solution, no solution, or infinitely many solutions. If the system has a solution, find it.

1. 
y = 6x + 1
y = 6x - 1

________________

2. 
y = 3x + 1
y = 2x - 1

________________



3. 
y = -5x + 1
y = -5x + 1

________________

4. 
y = 8x - 5
y = -8x - 5

________________



5. 
2y - 6x = 10 
2y + 6x = -10

________________

6. 
10y = 20x + 40
10y = 20x + 10

________________



7. 
y = (1/5)x - 2 
5y + 10 = x

________________

8. 
y = (1/4)x + 6 
4y - 24 = -x

________________

Solving systems of equations worksheets: a few things to keep in mind and/or remember.

Solving systems of linear equations worksheets

What is solving by the substitution method?

You can solve by substitution when you plug in either the value of x or the value of y into one of the two equations.

Example:

x = y + 1

y + x = 21

Here, you can just replace the value of x or y + 1 in y + x = 21

y + y + 1 = 21

2y + 1 = 21

2y = 20

y = 10 and x  = y + 1 = 10 + 1 = 11 

What is solving by elimination method?

You can solve by elimination when you eliminate either x or y by adding the two equations. We may need to rewrite one or both equations!

Example:

x = y + 1

y + x = 21

Let us rewrite x = y + 1 as x - y = 1 and then add the two equations to eliminate y.

x - y = 1

y + x = 21

Let us add the two equations.

2x - y + y = 1 + 21

2x + 0 = 22

2x = 22

x = 11

Using y + x = 21, y + 11 = 21, so y = 21 - 11 = 10.

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