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.

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

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

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

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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