Algebra 2 solving systems by substitution worksheet

One equation always has a variable on its own, so it can go straight into the other. Every system here has one whole-number solution, because the point is chosen before the equations are written.

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Sigma Prep · sigmaprep.io/worksheets Name Systems by Substitution Date Period Solve each system by substitution. $\begin{aligned} x & = 5 y + 53 \\ - 5 x + 3 y & = - 45 \end{aligned}$ $\begin{aligned} y & = - 3 x + 29 \\ - 2 x - y & = - 19 \end{aligned}$ $\begin{aligned} y & = - x + 4 \\ - 5 x + 3 y & = 28 \end{aligned}$ $\begin{aligned} x & = y - 9 \\ 4 x + 7 y & = - 3 \end{aligned}$ $\begin{aligned} y & = - 3 x - 10 \\ - 2 x + 5 y & = 35 \end{aligned}$ $\begin{aligned} y & = 5 x + 35 \\ - 7 x + 3 y & = 41 \end{aligned}$ $\begin{aligned} x & = 4 y - 20 \\ 6 x + y & = - 20 \end{aligned}$ $\begin{aligned} y & = 3 x + 38 \\ 5 x - 5 y & = - 90 \end{aligned}$ $\begin{aligned} x & = - 2 y - 7 \\ - 3 x - 5 y & = 13 \end{aligned}$ $\begin{aligned} y & = 5 x + 1 \\ - 2 x - 7 y & = - 7 \end{aligned}$ $\begin{aligned} x & = 2 y + 10 \\ - x - 3 y & = 25 \end{aligned}$ $\begin{aligned} y & = 3 x - 9 \\ - 6 x - 7 y & = - 45 \end{aligned}$ $\begin{aligned} y & = - x + 18 \\ 3 x + 7 y & = 86 \end{aligned}$ $\begin{aligned} x & = 4 y + 11 \\ - x - 3 y & = 24 \end{aligned}$ $\begin{aligned} x & = - 5 y - 19 \\ 5 x + 2 y & = - 3 \end{aligned}$ $\begin{aligned} y & = - 5 x - 14 \\ 2 x - y & = 0 \end{aligned}$ $\begin{aligned} y & = - x - 4 \\ 3 x + 4 y & = - 6 \end{aligned}$ $\begin{aligned} y & = - 3 x - 2 \\ 6 x - 2 y & = - 20 \end{aligned}$ $\begin{aligned} y & = - 3 x + 12 \\ 5 x - 3 y & = 6 \end{aligned}$ $\begin{aligned} x & = 3 y + 32 \\ x - 6 y & = 62 \end{aligned}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Systems by Substitution

Date Period

Solve each system by substitution.

$\begin{aligned} x & = 5 y + 53 \\ - 5 x + 3 y & = - 45 \end{aligned}$
$\begin{aligned} y & = - 3 x + 29 \\ - 2 x - y & = - 19 \end{aligned}$
$\begin{aligned} y & = - x + 4 \\ - 5 x + 3 y & = 28 \end{aligned}$
$\begin{aligned} x & = y - 9 \\ 4 x + 7 y & = - 3 \end{aligned}$
$\begin{aligned} y & = - 3 x - 10 \\ - 2 x + 5 y & = 35 \end{aligned}$
$\begin{aligned} y & = 5 x + 35 \\ - 7 x + 3 y & = 41 \end{aligned}$
$\begin{aligned} x & = 4 y - 20 \\ 6 x + y & = - 20 \end{aligned}$
$\begin{aligned} y & = 3 x + 38 \\ 5 x - 5 y & = - 90 \end{aligned}$
$\begin{aligned} x & = - 2 y - 7 \\ - 3 x - 5 y & = 13 \end{aligned}$
$\begin{aligned} y & = 5 x + 1 \\ - 2 x - 7 y & = - 7 \end{aligned}$
$\begin{aligned} x & = 2 y + 10 \\ - x - 3 y & = 25 \end{aligned}$
$\begin{aligned} y & = 3 x - 9 \\ - 6 x - 7 y & = - 45 \end{aligned}$
$\begin{aligned} y & = - x + 18 \\ 3 x + 7 y & = 86 \end{aligned}$
$\begin{aligned} x & = 4 y + 11 \\ - x - 3 y & = 24 \end{aligned}$
$\begin{aligned} x & = - 5 y - 19 \\ 5 x + 2 y & = - 3 \end{aligned}$
$\begin{aligned} y & = - 5 x - 14 \\ 2 x - y & = 0 \end{aligned}$
$\begin{aligned} y & = - x - 4 \\ 3 x + 4 y & = - 6 \end{aligned}$
$\begin{aligned} y & = - 3 x - 2 \\ 6 x - 2 y & = - 20 \end{aligned}$
$\begin{aligned} y & = - 3 x + 12 \\ 5 x - 3 y & = 6 \end{aligned}$
$\begin{aligned} x & = 3 y + 32 \\ x - 6 y & = 62 \end{aligned}$



Sigma Prep · sigmaprep.io/worksheets Name Systems by SubstitutionAnswer keyVersion 1 Date Period Solve each system by substitution. $\begin{aligned} x & = 5 y + 53 \\ - 5 x + 3 y & = - 45 \end{aligned}$ $(3, - 10)$ $\begin{aligned} y & = - 3 x + 29 \\ - 2 x - y & = - 19 \end{aligned}$ $(10, - 1)$ $\begin{aligned} y & = - x + 4 \\ - 5 x + 3 y & = 28 \end{aligned}$ $(- 2, 6)$ $\begin{aligned} x & = y - 9 \\ 4 x + 7 y & = - 3 \end{aligned}$ $(- 6, 3)$ $\begin{aligned} y & = - 3 x - 10 \\ - 2 x + 5 y & = 35 \end{aligned}$ $(- 5, 5)$ $\begin{aligned} y & = 5 x + 35 \\ - 7 x + 3 y & = 41 \end{aligned}$ $(- 8, - 5)$ $\begin{aligned} x & = 4 y - 20 \\ 6 x + y & = - 20 \end{aligned}$ $(- 4, 4)$ $\begin{aligned} y & = 3 x + 38 \\ 5 x - 5 y & = - 90 \end{aligned}$ $(- 10, 8)$ $\begin{aligned} x & = - 2 y - 7 \\ - 3 x - 5 y & = 13 \end{aligned}$ $(9, - 8)$ $\begin{aligned} y & = 5 x + 1 \\ - 2 x - 7 y & = - 7 \end{aligned}$ $(0, 1)$ $\begin{aligned} x & = 2 y + 10 \\ - x - 3 y & = 25 \end{aligned}$ $(- 4, - 7)$ $\begin{aligned} y & = 3 x - 9 \\ - 6 x - 7 y & = - 45 \end{aligned}$ $(4, 3)$ $\begin{aligned} y & = - x + 18 \\ 3 x + 7 y & = 86 \end{aligned}$ $(10, 8)$ $\begin{aligned} x & = 4 y + 11 \\ - x - 3 y & = 24 \end{aligned}$ $(- 9, - 5)$ $\begin{aligned} x & = - 5 y - 19 \\ 5 x + 2 y & = - 3 \end{aligned}$ $(1, - 4)$ $\begin{aligned} y & = - 5 x - 14 \\ 2 x - y & = 0 \end{aligned}$ $(- 2, - 4)$ $\begin{aligned} y & = - x - 4 \\ 3 x + 4 y & = - 6 \end{aligned}$ $(- 10, 6)$ $\begin{aligned} y & = - 3 x - 2 \\ 6 x - 2 y & = - 20 \end{aligned}$ $(- 2, 4)$ $\begin{aligned} y & = - 3 x + 12 \\ 5 x - 3 y & = 6 \end{aligned}$ $(3, 3)$ $\begin{aligned} x & = 3 y + 32 \\ x - 6 y & = 62 \end{aligned}$ $(2, - 10)$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Systems by SubstitutionAnswer keyVersion 1

Date Period

Solve each system by substitution.

$\begin{aligned} x & = 5 y + 53 \\ - 5 x + 3 y & = - 45 \end{aligned}$ $(3, - 10)$
$\begin{aligned} y & = - 3 x + 29 \\ - 2 x - y & = - 19 \end{aligned}$ $(10, - 1)$
$\begin{aligned} y & = - x + 4 \\ - 5 x + 3 y & = 28 \end{aligned}$ $(- 2, 6)$
$\begin{aligned} x & = y - 9 \\ 4 x + 7 y & = - 3 \end{aligned}$ $(- 6, 3)$
$\begin{aligned} y & = - 3 x - 10 \\ - 2 x + 5 y & = 35 \end{aligned}$ $(- 5, 5)$
$\begin{aligned} y & = 5 x + 35 \\ - 7 x + 3 y & = 41 \end{aligned}$ $(- 8, - 5)$
$\begin{aligned} x & = 4 y - 20 \\ 6 x + y & = - 20 \end{aligned}$ $(- 4, 4)$
$\begin{aligned} y & = 3 x + 38 \\ 5 x - 5 y & = - 90 \end{aligned}$ $(- 10, 8)$
$\begin{aligned} x & = - 2 y - 7 \\ - 3 x - 5 y & = 13 \end{aligned}$ $(9, - 8)$
$\begin{aligned} y & = 5 x + 1 \\ - 2 x - 7 y & = - 7 \end{aligned}$ $(0, 1)$
$\begin{aligned} x & = 2 y + 10 \\ - x - 3 y & = 25 \end{aligned}$ $(- 4, - 7)$
$\begin{aligned} y & = 3 x - 9 \\ - 6 x - 7 y & = - 45 \end{aligned}$ $(4, 3)$
$\begin{aligned} y & = - x + 18 \\ 3 x + 7 y & = 86 \end{aligned}$ $(10, 8)$
$\begin{aligned} x & = 4 y + 11 \\ - x - 3 y & = 24 \end{aligned}$ $(- 9, - 5)$
$\begin{aligned} x & = - 5 y - 19 \\ 5 x + 2 y & = - 3 \end{aligned}$ $(1, - 4)$
$\begin{aligned} y & = - 5 x - 14 \\ 2 x - y & = 0 \end{aligned}$ $(- 2, - 4)$
$\begin{aligned} y & = - x - 4 \\ 3 x + 4 y & = - 6 \end{aligned}$ $(- 10, 6)$
$\begin{aligned} y & = - 3 x - 2 \\ 6 x - 2 y & = - 20 \end{aligned}$ $(- 2, 4)$
$\begin{aligned} y & = - 3 x + 12 \\ 5 x - 3 y & = 6 \end{aligned}$ $(3, 3)$
$\begin{aligned} x & = 3 y + 32 \\ x - 6 y & = 62 \end{aligned}$ $(2, - 10)$

How to do these

$\begin{aligned} x + 3 y & = 9 \\ 2 x - y & = 4 \end{aligned}$

The first gives x = 9 - 3y.
Put that into the second: 2(9 - 3y) - y = 4.
18 - 7y = 4, so y = 2 and x = 3.

The answer is $(3, 2)$ .

Where students go wrong

Substituting back into the same equation you rearranged. That collapses to something true and useless like 9 = 9. The rearranged expression has to go into the OTHER equation.

Also called substitution method, solving systems by substituting or systems of equations.

What you can put on this worksheet

One variable already alone: $\begin{aligned} x & = - 2 y + 2 \\ 3 x + y & = 1 \end{aligned}$ → $(0, 1)$
Two y= lines, a constant line, or y = kx: $\begin{aligned} y & = 4 x \\ 2 x + 5 y & = - 22 \end{aligned}$ → $(- 1, - 4)$
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 substitution: ${\begin{cases} y = - 3 x - 6 \\ 6 x + 2 y = - 12 \end{cases}$ → Infinitely many solutions
Neither equation has a coefficient of 1: $\begin{aligned} - 3 x - 4 y & = 28 \\ 3 x - 4 y & = 4 \end{aligned}$ → $(- 4, - 4)$

Questions about these worksheets

Yes. Every solving systems by substitution 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 substitution 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: one variable already alone, two y= lines, a constant line, or y = kx, one, none or infinitely many solutions, mix in some with no solution or infinitely many and neither equation has a coefficient of 1. Tick as many as you want and set how many of each, or let it spread them evenly.

Substituting back into the same equation you rearranged. That collapses to something true and useless like 9 = 9. The rearranged expression has to go into the OTHER equation.

Algebra 2 solving systems by substitution worksheet

Select your difficulty

Systems by Substitution

Systems by SubstitutionAnswer keyVersion 1

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

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