Algebra 2 solving systems by elimination worksheet

Multiply one or both equations so a variable cancels when you add them. Also called the addition method, which is exactly what it is.

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Sigma Prep · sigmaprep.io/worksheets Name Systems by Elimination Date Period Solve each system by elimination. $\begin{aligned} 7 x + 2 y & = 1 \\ 6 x + 4 y & = - 22 \end{aligned}$ $\begin{aligned} - 3 x - 2 y & = 3 \\ - x - 4 y & = 1 \end{aligned}$ $\begin{aligned} - 3 x + 6 y & = - 24 \\ - 2 x + 18 y & = - 100 \end{aligned}$ $\begin{aligned} 4 x + 7 y & = - 22 \\ - 6 x - 14 y & = 54 \end{aligned}$ $\begin{aligned} - 6 x + y & = 7 \\ - x + 3 y & = - 13 \end{aligned}$ $\begin{aligned} 3 x - 5 y & = - 65 \\ 7 x - 15 y & = - 185 \end{aligned}$ $\begin{aligned} - x + 3 y & = 20 \\ 4 x + 9 y & = 109 \end{aligned}$ $\begin{aligned} x + 2 y & = 1 \\ - x - 4 y & = - 9 \end{aligned}$ $\begin{aligned} x + 6 y & = 3 \\ - 2 x + 12 y & = - 6 \end{aligned}$ $\begin{aligned} 4 x - y & = - 9 \\ - x - 2 y & = 18 \end{aligned}$ $\begin{aligned} 4 x - 6 y & = 60 \\ - 7 x - 18 y & = 123 \end{aligned}$ $\begin{aligned} - 7 x - 6 y & = 112 \\ x - 12 y & = 74 \end{aligned}$ $\begin{aligned} - x - 3 y & = - 24 \\ 7 x + 9 y & = 96 \end{aligned}$ $\begin{aligned} - 3 x - 2 y & = - 17 \\ - 7 x + 6 y & = 3 \end{aligned}$ $\begin{aligned} - 6 x - 2 y & = 42 \\ - 6 x - 4 y & = 60 \end{aligned}$ $\begin{aligned} 3 x - 4 y & = 11 \\ 6 x + 8 y & = - 10 \end{aligned}$ $\begin{aligned} - 3 x - 7 y & = - 30 \\ 3 x - 14 y & = - 33 \end{aligned}$ $\begin{aligned} 4 x + y & = - 31 \\ - 6 x + 2 y & = 78 \end{aligned}$ $\begin{aligned} - 4 x + y & = 23 \\ - 2 x - 3 y & = 1 \end{aligned}$ $\begin{aligned} 2 x - 7 y & = 23 \\ x + 21 y & = - 62 \end{aligned}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Systems by Elimination

Date Period

Solve each system by elimination.

$\begin{aligned} 7 x + 2 y & = 1 \\ 6 x + 4 y & = - 22 \end{aligned}$
$\begin{aligned} - 3 x - 2 y & = 3 \\ - x - 4 y & = 1 \end{aligned}$
$\begin{aligned} - 3 x + 6 y & = - 24 \\ - 2 x + 18 y & = - 100 \end{aligned}$
$\begin{aligned} 4 x + 7 y & = - 22 \\ - 6 x - 14 y & = 54 \end{aligned}$
$\begin{aligned} - 6 x + y & = 7 \\ - x + 3 y & = - 13 \end{aligned}$
$\begin{aligned} 3 x - 5 y & = - 65 \\ 7 x - 15 y & = - 185 \end{aligned}$
$\begin{aligned} - x + 3 y & = 20 \\ 4 x + 9 y & = 109 \end{aligned}$
$\begin{aligned} x + 2 y & = 1 \\ - x - 4 y & = - 9 \end{aligned}$
$\begin{aligned} x + 6 y & = 3 \\ - 2 x + 12 y & = - 6 \end{aligned}$
$\begin{aligned} 4 x - y & = - 9 \\ - x - 2 y & = 18 \end{aligned}$
$\begin{aligned} 4 x - 6 y & = 60 \\ - 7 x - 18 y & = 123 \end{aligned}$
$\begin{aligned} - 7 x - 6 y & = 112 \\ x - 12 y & = 74 \end{aligned}$
$\begin{aligned} - x - 3 y & = - 24 \\ 7 x + 9 y & = 96 \end{aligned}$
$\begin{aligned} - 3 x - 2 y & = - 17 \\ - 7 x + 6 y & = 3 \end{aligned}$
$\begin{aligned} - 6 x - 2 y & = 42 \\ - 6 x - 4 y & = 60 \end{aligned}$
$\begin{aligned} 3 x - 4 y & = 11 \\ 6 x + 8 y & = - 10 \end{aligned}$
$\begin{aligned} - 3 x - 7 y & = - 30 \\ 3 x - 14 y & = - 33 \end{aligned}$
$\begin{aligned} 4 x + y & = - 31 \\ - 6 x + 2 y & = 78 \end{aligned}$
$\begin{aligned} - 4 x + y & = 23 \\ - 2 x - 3 y & = 1 \end{aligned}$
$\begin{aligned} 2 x - 7 y & = 23 \\ x + 21 y & = - 62 \end{aligned}$



Sigma Prep · sigmaprep.io/worksheets Name Systems by EliminationAnswer keyVersion 1 Date Period Solve each system by elimination. $\begin{aligned} 7 x + 2 y & = 1 \\ 6 x + 4 y & = - 22 \end{aligned}$ $(3, - 10)$ $\begin{aligned} - 3 x - 2 y & = 3 \\ - x - 4 y & = 1 \end{aligned}$ $(- 1, 0)$ $\begin{aligned} - 3 x + 6 y & = - 24 \\ - 2 x + 18 y & = - 100 \end{aligned}$ $(- 4, - 6)$ $\begin{aligned} 4 x + 7 y & = - 22 \\ - 6 x - 14 y & = 54 \end{aligned}$ $(5, - 6)$ $\begin{aligned} - 6 x + y & = 7 \\ - x + 3 y & = - 13 \end{aligned}$ $(- 2, - 5)$ $\begin{aligned} 3 x - 5 y & = - 65 \\ 7 x - 15 y & = - 185 \end{aligned}$ $(- 5, 10)$ $\begin{aligned} - x + 3 y & = 20 \\ 4 x + 9 y & = 109 \end{aligned}$ $(7, 9)$ $\begin{aligned} x + 2 y & = 1 \\ - x - 4 y & = - 9 \end{aligned}$ $(- 7, 4)$ $\begin{aligned} x + 6 y & = 3 \\ - 2 x + 12 y & = - 6 \end{aligned}$ $(3, 0)$ $\begin{aligned} 4 x - y & = - 9 \\ - x - 2 y & = 18 \end{aligned}$ $(- 4, - 7)$ $\begin{aligned} 4 x - 6 y & = 60 \\ - 7 x - 18 y & = 123 \end{aligned}$ $(3, - 8)$ $\begin{aligned} - 7 x - 6 y & = 112 \\ x - 12 y & = 74 \end{aligned}$ $(- 10, - 7)$ $\begin{aligned} - x - 3 y & = - 24 \\ 7 x + 9 y & = 96 \end{aligned}$ $(6, 6)$ $\begin{aligned} - 3 x - 2 y & = - 17 \\ - 7 x + 6 y & = 3 \end{aligned}$ $(3, 4)$ $\begin{aligned} - 6 x - 2 y & = 42 \\ - 6 x - 4 y & = 60 \end{aligned}$ $(- 4, - 9)$ $\begin{aligned} 3 x - 4 y & = 11 \\ 6 x + 8 y & = - 10 \end{aligned}$ $(1, - 2)$ $\begin{aligned} - 3 x - 7 y & = - 30 \\ 3 x - 14 y & = - 33 \end{aligned}$ $(3, 3)$ $\begin{aligned} 4 x + y & = - 31 \\ - 6 x + 2 y & = 78 \end{aligned}$ $(- 10, 9)$ $\begin{aligned} - 4 x + y & = 23 \\ - 2 x - 3 y & = 1 \end{aligned}$ $(- 5, 3)$ $\begin{aligned} 2 x - 7 y & = 23 \\ x + 21 y & = - 62 \end{aligned}$ $(1, - 3)$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Systems by EliminationAnswer keyVersion 1

Date Period

Solve each system by elimination.

$\begin{aligned} 7 x + 2 y & = 1 \\ 6 x + 4 y & = - 22 \end{aligned}$ $(3, - 10)$
$\begin{aligned} - 3 x - 2 y & = 3 \\ - x - 4 y & = 1 \end{aligned}$ $(- 1, 0)$
$\begin{aligned} - 3 x + 6 y & = - 24 \\ - 2 x + 18 y & = - 100 \end{aligned}$ $(- 4, - 6)$
$\begin{aligned} 4 x + 7 y & = - 22 \\ - 6 x - 14 y & = 54 \end{aligned}$ $(5, - 6)$
$\begin{aligned} - 6 x + y & = 7 \\ - x + 3 y & = - 13 \end{aligned}$ $(- 2, - 5)$
$\begin{aligned} 3 x - 5 y & = - 65 \\ 7 x - 15 y & = - 185 \end{aligned}$ $(- 5, 10)$
$\begin{aligned} - x + 3 y & = 20 \\ 4 x + 9 y & = 109 \end{aligned}$ $(7, 9)$
$\begin{aligned} x + 2 y & = 1 \\ - x - 4 y & = - 9 \end{aligned}$ $(- 7, 4)$
$\begin{aligned} x + 6 y & = 3 \\ - 2 x + 12 y & = - 6 \end{aligned}$ $(3, 0)$
$\begin{aligned} 4 x - y & = - 9 \\ - x - 2 y & = 18 \end{aligned}$ $(- 4, - 7)$
$\begin{aligned} 4 x - 6 y & = 60 \\ - 7 x - 18 y & = 123 \end{aligned}$ $(3, - 8)$
$\begin{aligned} - 7 x - 6 y & = 112 \\ x - 12 y & = 74 \end{aligned}$ $(- 10, - 7)$
$\begin{aligned} - x - 3 y & = - 24 \\ 7 x + 9 y & = 96 \end{aligned}$ $(6, 6)$
$\begin{aligned} - 3 x - 2 y & = - 17 \\ - 7 x + 6 y & = 3 \end{aligned}$ $(3, 4)$
$\begin{aligned} - 6 x - 2 y & = 42 \\ - 6 x - 4 y & = 60 \end{aligned}$ $(- 4, - 9)$
$\begin{aligned} 3 x - 4 y & = 11 \\ 6 x + 8 y & = - 10 \end{aligned}$ $(1, - 2)$
$\begin{aligned} - 3 x - 7 y & = - 30 \\ 3 x - 14 y & = - 33 \end{aligned}$ $(3, 3)$
$\begin{aligned} 4 x + y & = - 31 \\ - 6 x + 2 y & = 78 \end{aligned}$ $(- 10, 9)$
$\begin{aligned} - 4 x + y & = 23 \\ - 2 x - 3 y & = 1 \end{aligned}$ $(- 5, 3)$
$\begin{aligned} 2 x - 7 y & = 23 \\ x + 21 y & = - 62 \end{aligned}$ $(1, - 3)$

How to do these

Solve $3 x + 2 y = 16$ and $3 x - y = 4$

The x terms already match.
Subtract the second from the first to remove x.
3y = 12, so y = 4 and x = 4.

The answer is $(4, 4)$ .

Where students go wrong

Adding when you should subtract. The coefficients have to be opposites for adding to cancel them, so matching coefficients means subtracting. Writing the signs out before you combine prevents most of it.

Also called addition method, elimination method, linear combination or systems of equations.

What you can put on this worksheet

Lined up to add or subtract: $\begin{aligned} x - 3 y & = - 3 \\ - 4 x + 3 y & = 3 \end{aligned}$ → $(0, 1)$
Rearrange first, then eliminate: $\begin{array}{r} x = 4 y - 4 \\ - 6 y = - 6 + 6 x \end{array}$ → $(0, 1)$
One, none or infinitely many solutions: How many solutions: $y = 3 x - 5$ and $y = 3 x + 3$ → No solution
Mix in some with no solution or infinitely many: Solve by elimination: ${\begin{cases} 3 x - 2 y = 3 \\ 9 x - 6 y = 9 \end{cases}$ → Infinitely many solutions
Fraction coefficients: Solve by elimination:
$- \frac{2}{3} x + \frac{1}{3} y = \frac{1}{3}$
$\frac{5}{9} x + \frac{7}{9} y = \frac{7}{9}$ → $(0, 1)$

Questions about these worksheets

Yes. Every solving systems by elimination sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 2 is usually taken around 10th or 11th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the solving systems by elimination questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 5: lined up to add or subtract, rearrange first, then eliminate, one, none or infinitely many solutions, mix in some with no solution or infinitely many and fraction coefficients. Tick as many as you want and set how many of each, or let it spread them evenly.

Algebra 2 solving systems by elimination worksheet

Select your difficulty

Systems by Elimination

Systems by EliminationAnswer keyVersion 1

How to do these

Where students go wrong

What you can put on this worksheet

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