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Printable “System of Equations” worksheets:

Solve Systems of Equations with Substitution

Solve Systems of Equations with Elimination

Solve Systems of Equation Word Problems

System of Equations using the Graphical Method

System of Equations Word Problems using the Graphical Method

System of Equations with No Solution

Examples, solutions, videos, and worksheets to help Grade 7 and Grade 8 learn that a system of linear equations whose graphs are parallel lines will have no solution because parallel lines do not intersect. Parallel lines have the same slope but no common point. One can verify that two lines are parallel by comparing their slopes and their y-intercept points.

A system of equations with no solution occurs when the two lines represented by the equations are parallel and do not intersect. This means that there is no point that satisfies both equations simultaneously.

Graphically:

When the lines are parallel, they have the same slope but different y-intercepts.

Since they never cross, there is no point that lies on both lines.

Algebraically:

When solving the system algebraically, you will reach a contradiction, such as 0 = 5. This indicates that there is no solution.

A system of equations has no solution when the lines are parallel, which happens if the slopes (𝑚) of the two lines are the same but the y-intercepts (𝑏) are different.

If the slope and y-intercepts are the same then the equations represent the same line and there are infinite number of solutions.

Have a look at this video if you need to review how to graph systems of Equations with infinitely many or no solutions.

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(Answers on the second page.)

System of Equations Worksheet #1

System of Equations Worksheet #2

System of Equations Worksheet #3

System of Equations Worksheet #4

System of Equations Worksheet #5

System of Equation with No Solution

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