Systems of Linear Equations Practice Worksheet

Practice solving systems of equations using substitution and elimination methods.

Solve each system carefully and check your solution in both equations.

Download Printable PDF

Level 1: Substitution Method

Problem 1
\[ \begin{cases} y = x + 2 \\ y = 5 \end{cases} \]
Show solution

Substitute \(y=5\) into the first equation.

\[ 5 = x + 2 \]
\[ x = 3 \]

Solution:

\[ (3,5) \]
Problem 2
\[ \begin{cases} y = 2x + 1 \\ y = x + 4 \end{cases} \]
Show solution

Set the equations equal to each other.

\[ 2x + 1 = x + 4 \]
\[ x = 3 \]

Substitute back into either equation.

\[ y = 2(3)+1 = 7 \]
\[ (3,7) \]
Problem 3
\[ \begin{cases} x + y = 9 \\ y = x + 1 \end{cases} \]
Show solution

Substitute \(y=x+1\) into the first equation.

\[ x + (x+1)=9 \]
\[ 2x+1=9 \]
\[ 2x=8 \]
\[ x=4 \]
\[ y=5 \]
\[ (4,5) \]

Level 2: Elimination Method

Problem 4
\[ \begin{cases} x+y=10 \\ x-y=2 \end{cases} \]
Show solution

Add the equations together.

\[ 2x=12 \]
\[ x=6 \]

Substitute back into an equation.

\[ 6+y=10 \]
\[ y=4 \]
\[ (6,4) \]
Problem 5
\[ \begin{cases} 2x+y=9 \\ x-y=0 \end{cases} \]
Show solution

Add the equations together.

\[ 3x=9 \]
\[ x=3 \]

Substitute back.

\[ y=3 \]
\[ (3,3) \]
Problem 6
\[ \begin{cases} 3x+2y=16 \\ 3x-2y=8 \end{cases} \]
Show solution

Add the equations together.

\[ 6x=24 \]
\[ x=4 \]

Substitute back into an equation.

\[ 3(4)+2y=16 \]
\[ 12+2y=16 \]
\[ y=2 \]
\[ (4,2) \]

Related Algebra Resources

Systems of Linear Equations Explained

Review substitution and elimination methods with worked examples.

Graphing Linear Functions

Learn how systems relate to linear graphs, slope, and intersections.

Contact me to get started

Support Free Math Resources

Find this resource helpful?

RaulTheTutor.com provides free interactive tools, guides, reference resources, and practice materials for students, parents, and teachers. If this resource helped you, consider making an optional contribution to support the development of more free math resources.

Support Free Math Resources