Solving systems of equations worksheets

Solving systems of equations worksheets on this page. Find out below how you can 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 substitution?

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?

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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