Allday Education

Free Systems of Equations Worksheet

Ten two-variable systems with whole-number solutions, solvable by substitution or elimination, plus a key with each (x, y) pair.

Answer key included
Name: Date:
Systems of Equations
1.
{3x4y=62x+2y=10\begin{cases} 3x - 4y = -6 \\ 2x + 2y = 10 \end{cases}
2.
{2x4y=162x+5y=20\begin{cases} 2x - 4y = 16 \\ 2x + 5y = -20 \end{cases}
3.
{2x+3y=162x3y=4\begin{cases} 2x + 3y = -16 \\ 2x - 3y = -4 \end{cases}
4.
{2x+3y=135xy=27\begin{cases} 2x + 3y = -13 \\ 5x - y = 27 \end{cases}
5.
{4x+y=124x4y=12\begin{cases} 4x + y = -12 \\ 4x - 4y = -12 \end{cases}
6.
{5x+y=10x+3y=12\begin{cases} 5x + y = 10 \\ x + 3y = -12 \end{cases}
7.
{x+5y=44x3y=7\begin{cases} x + 5y = -4 \\ 4x - 3y = 7 \end{cases}
8.
{4x2y=102x+3y=1\begin{cases} 4x - 2y = -10 \\ 2x + 3y = -1 \end{cases}
9.
{2x+y=193x+y=26\begin{cases} 2x + y = 19 \\ 3x + y = 26 \end{cases}
10.
{5x+2y=53x+3y=6\begin{cases} 5x + 2y = 5 \\ 3x + 3y = -6 \end{cases}
Andy · alldayeverydaymath.com
Name: Answer KeyDate:
Systems of Equations
1.
{3x4y=62x+2y=10\begin{cases} 3x - 4y = -6 \\ 2x + 2y = 10 \end{cases}
Answer: x=2,y=3x = 2, y = 3
2.
{2x4y=162x+5y=20\begin{cases} 2x - 4y = 16 \\ 2x + 5y = -20 \end{cases}
Answer: x=0,y=4x = 0, y = -4
3.
{2x+3y=162x3y=4\begin{cases} 2x + 3y = -16 \\ 2x - 3y = -4 \end{cases}
Answer: x=5,y=2x = -5, y = -2
4.
{2x+3y=135xy=27\begin{cases} 2x + 3y = -13 \\ 5x - y = 27 \end{cases}
Answer: x=4,y=7x = 4, y = -7
5.
{4x+y=124x4y=12\begin{cases} 4x + y = -12 \\ 4x - 4y = -12 \end{cases}
Answer: x=3,y=0x = -3, y = 0
6.
{5x+y=10x+3y=12\begin{cases} 5x + y = 10 \\ x + 3y = -12 \end{cases}
Answer: x=3,y=5x = 3, y = -5
7.
{x+5y=44x3y=7\begin{cases} x + 5y = -4 \\ 4x - 3y = 7 \end{cases}
Answer: x=1,y=1x = 1, y = -1
8.
{4x2y=102x+3y=1\begin{cases} 4x - 2y = -10 \\ 2x + 3y = -1 \end{cases}
Answer: x=2,y=1x = -2, y = 1
9.
{2x+y=193x+y=26\begin{cases} 2x + y = 19 \\ 3x + y = 26 \end{cases}
Answer: x=7,y=5x = 7, y = 5
10.
{5x+2y=53x+3y=6\begin{cases} 5x + 2y = 5 \\ 3x + 3y = -6 \end{cases}
Answer: x=3,y=5x = 3, y = -5
Andy · alldayeverydaymath.com

Scroll to see all 10 problems and the answer key on its own page. Printing includes every page.

About this worksheet

Each system is constructed from a chosen solution point, so elimination and substitution both land on clean integers. Great as mixed practice once both methods have been taught — students can pick their method and still check against one key.

Students shaky on the skill itself? Send them to the free lesson: Systems of Equations — explained step by step.

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