Graph y ≤ 4x - 15 and y ≥ 2x - 11

the overlap, cornered at (2, -7)

Graph y > -2x - 2 and y ≥ -x - 1

the overlap, cornered at (-1, 0)

Graph y > -2x - 11 and y ≤ 4x + 7

the overlap, cornered at (-3, -5)

Graph y ≥ 2x - 13 and y > 4x - 21

the overlap, cornered at (4, -5)

Graph y > -3x - 7 and y ≤ x - 3

the overlap, cornered at (-1, -4)

Graph y ≤ 2x + 15 and y ≤ -3x - 5

the overlap, cornered at (-4, 7)

Graph y ≤ -x + 12 and y ≤ 2x - 3

the overlap, cornered at (5, 7)

Graph y > x + 8 and y ≤ -x - 2

the overlap, cornered at (-5, 3)

Graph y ≥ 4x - 6 and y > -x - 6

the overlap, cornered at (0, -6)

Graph y < -x + 3 and y ≤ -3x + 7

the overlap, cornered at (2, 1)

Graph y > -4x - 12 and y ≥ 4x + 20

the overlap, cornered at (-4, 4)

Graph y ≤ x + 6 and y > -4x - 9

the overlap, cornered at (-3, 3)

Graph y ≤ 2x + 9 and y > 4x + 19

the overlap, cornered at (-5, -1)

Graph y > -4x - 16 and y ≥ x - 1

the overlap, cornered at (-3, -4)

Graph y < -4x - 12 and y ≥ 2x

the overlap, cornered at (-2, -4)

Graph y > -x + 8 and y ≥ 3x - 8

the overlap, cornered at (4, 4)

Graph y ≤ -3x + 4 and y < -4x + 6

the overlap, cornered at (2, -2)

Graph y > -3x - 13 and y < x + 11

the overlap, cornered at (-6, 5)

Graph y < 2x - 2 and y < -4x - 2

the overlap, cornered at (0, -2)

Graph y ≥ 2x + 6 and y ≤ x + 4

the overlap, cornered at (-2, 2)

Worksheets · Precalculus

Precalculus systems of inequalities worksheet

Q: Are these systems of inequalities worksheets free?

Yes. Every systems of inequalities 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.

Q: Do the systems of inequalities worksheets come with an answer key?

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.

Q: Are these systems of inequalities worksheets printable?

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.

Q: What grade are these systems of inequalities worksheets for?

Precalculus is usually taken around 11th or 12th 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.

Q: Can I get a different version of the same systems of inequalities worksheet?

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.

Q: Is this a free alternative to Kuta Software for systems of inequalities?

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 systems of inequalities 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.

Q: Can I choose how hard the systems of inequalities questions are?

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.

Q: What do students get wrong with systems of inequalities?

Giving the whole shaded area rather than the overlap. Only the part covered by both counts, and it is easy to lose track once two greys sit on top of each other. Shading lightly, or with lines in two directions, keeps it readable.

Shade each inequality, and the solution is the part shaded twice. Everything from the single-inequality sheet applies, done twice and then intersected.



Sigma Prep · sigmaprep.io/worksheets Name Systems of Inequalities Date Period Graph each system. Graph $y \leq 4 x - 15$ and $y \geq 2 x - 11$ -10-10-5-55510100 Graph $y > - 2 x - 2$ and $y \geq - x - 1$ -10-10-5-55510100 Graph $y > - 2 x - 11$ and $y \leq 4 x + 7$ -10-10-5-55510100 Graph $y \geq 2 x - 13$ and $y > 4 x - 21$ -10-10-5-55510100 Graph $y > - 3 x - 7$ and $y \leq x - 3$ -10-10-5-55510100 Graph $y \leq 2 x + 15$ and $y \leq - 3 x - 5$ -10-10-5-55510100 Graph $y \leq - x + 12$ and $y \leq 2 x - 3$ -10-10-5-55510100 Graph $y > x + 8$ and $y \leq - x - 2$ -10-10-5-55510100 Graph $y \geq 4 x - 6$ and $y > - x - 6$ -10-10-5-55510100 Graph $y < - x + 3$ and $y \leq - 3 x + 7$ -10-10-5-55510100 Graph $y > - 4 x - 12$ and $y \geq 4 x + 20$ -10-10-5-55510100 Graph $y \leq x + 6$ and $y > - 4 x - 9$ -10-10-5-55510100 Graph $y \leq 2 x + 9$ and $y > 4 x + 19$ -10-10-5-55510100 Graph $y > - 4 x - 16$ and $y \geq x - 1$ -10-10-5-55510100 Graph $y < - 4 x - 12$ and $y \geq 2 x$ -10-10-5-55510100 Graph $y > - x + 8$ and $y \geq 3 x - 8$ -10-10-5-55510100 Graph $y \leq - 3 x + 4$ and $y < - 4 x + 6$ -10-10-5-55510100 Graph $y > - 3 x - 13$ and $y < x + 11$ -10-10-5-55510100 Graph $y < 2 x - 2$ and $y < - 4 x - 2$ -10-10-5-55510100 Graph $y \geq 2 x + 6$ and $y \leq x + 4$ -10-10-5-55510100 Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Systems of Inequalities

Date Period

Graph each system.

Graph $y \leq 4 x - 15$ and $y \geq 2 x - 11$ -10-10-5-55510100
Graph $y > - 2 x - 2$ and $y \geq - x - 1$ -10-10-5-55510100
Graph $y > - 2 x - 11$ and $y \leq 4 x + 7$ -10-10-5-55510100
Graph $y \geq 2 x - 13$ and $y > 4 x - 21$ -10-10-5-55510100
Graph $y > - 3 x - 7$ and $y \leq x - 3$ -10-10-5-55510100
Graph $y \leq 2 x + 15$ and $y \leq - 3 x - 5$ -10-10-5-55510100
Graph $y \leq - x + 12$ and $y \leq 2 x - 3$ -10-10-5-55510100
Graph $y > x + 8$ and $y \leq - x - 2$ -10-10-5-55510100
Graph $y \geq 4 x - 6$ and $y > - x - 6$ -10-10-5-55510100
Graph $y < - x + 3$ and $y \leq - 3 x + 7$ -10-10-5-55510100
Graph $y > - 4 x - 12$ and $y \geq 4 x + 20$ -10-10-5-55510100
Graph $y \leq x + 6$ and $y > - 4 x - 9$ -10-10-5-55510100
Graph $y \leq 2 x + 9$ and $y > 4 x + 19$ -10-10-5-55510100
Graph $y > - 4 x - 16$ and $y \geq x - 1$ -10-10-5-55510100
Graph $y < - 4 x - 12$ and $y \geq 2 x$ -10-10-5-55510100
Graph $y > - x + 8$ and $y \geq 3 x - 8$ -10-10-5-55510100
Graph $y \leq - 3 x + 4$ and $y < - 4 x + 6$ -10-10-5-55510100
Graph $y > - 3 x - 13$ and $y < x + 11$ -10-10-5-55510100
Graph $y < 2 x - 2$ and $y < - 4 x - 2$ -10-10-5-55510100
Graph $y \geq 2 x + 6$ and $y \leq x + 4$ -10-10-5-55510100



Sigma Prep · sigmaprep.io/worksheets Name Systems of InequalitiesAnswer keyVersion 1 Date Period Graph each system. Graph $y \leq 4 x - 15$ and $y \geq 2 x - 11$ -10-10-5-55510100the overlap, cornered at $(2, - 7)$ Graph $y > - 2 x - 2$ and $y \geq - x - 1$ -10-10-5-55510100the overlap, cornered at $(- 1, 0)$ Graph $y > - 2 x - 11$ and $y \leq 4 x + 7$ -10-10-5-55510100the overlap, cornered at $(- 3, - 5)$ Graph $y \geq 2 x - 13$ and $y > 4 x - 21$ -10-10-5-55510100the overlap, cornered at $(4, - 5)$ Graph $y > - 3 x - 7$ and $y \leq x - 3$ -10-10-5-55510100the overlap, cornered at $(- 1, - 4)$ Graph $y \leq 2 x + 15$ and $y \leq - 3 x - 5$ -10-10-5-55510100the overlap, cornered at $(- 4, 7)$ Graph $y \leq - x + 12$ and $y \leq 2 x - 3$ -10-10-5-55510100the overlap, cornered at $(5, 7)$ Graph $y > x + 8$ and $y \leq - x - 2$ -10-10-5-55510100the overlap, cornered at $(- 5, 3)$ Graph $y \geq 4 x - 6$ and $y > - x - 6$ -10-10-5-55510100the overlap, cornered at $(0, - 6)$ Graph $y < - x + 3$ and $y \leq - 3 x + 7$ -10-10-5-55510100the overlap, cornered at $(2, 1)$ Graph $y > - 4 x - 12$ and $y \geq 4 x + 20$ -10-10-5-55510100the overlap, cornered at $(- 4, 4)$ Graph $y \leq x + 6$ and $y > - 4 x - 9$ -10-10-5-55510100the overlap, cornered at $(- 3, 3)$ Graph $y \leq 2 x + 9$ and $y > 4 x + 19$ -10-10-5-55510100the overlap, cornered at $(- 5, - 1)$ Graph $y > - 4 x - 16$ and $y \geq x - 1$ -10-10-5-55510100the overlap, cornered at $(- 3, - 4)$ Graph $y < - 4 x - 12$ and $y \geq 2 x$ -10-10-5-55510100the overlap, cornered at $(- 2, - 4)$ Graph $y > - x + 8$ and $y \geq 3 x - 8$ -10-10-5-55510100the overlap, cornered at $(4, 4)$ Graph $y \leq - 3 x + 4$ and $y < - 4 x + 6$ -10-10-5-55510100the overlap, cornered at $(2, - 2)$ Graph $y > - 3 x - 13$ and $y < x + 11$ -10-10-5-55510100the overlap, cornered at $(- 6, 5)$ Graph $y < 2 x - 2$ and $y < - 4 x - 2$ -10-10-5-55510100the overlap, cornered at $(0, - 2)$ Graph $y \geq 2 x + 6$ and $y \leq x + 4$ -10-10-5-55510100the overlap, cornered at $(- 2, 2)$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Systems of InequalitiesAnswer keyVersion 1

Date Period

Graph each system.

Graph $y \leq 4 x - 15$ and $y \geq 2 x - 11$ -10-10-5-55510100the overlap, cornered at $(2, - 7)$
Graph $y > - 2 x - 2$ and $y \geq - x - 1$ -10-10-5-55510100the overlap, cornered at $(- 1, 0)$
Graph $y > - 2 x - 11$ and $y \leq 4 x + 7$ -10-10-5-55510100the overlap, cornered at $(- 3, - 5)$
Graph $y \geq 2 x - 13$ and $y > 4 x - 21$ -10-10-5-55510100the overlap, cornered at $(4, - 5)$
Graph $y > - 3 x - 7$ and $y \leq x - 3$ -10-10-5-55510100the overlap, cornered at $(- 1, - 4)$
Graph $y \leq 2 x + 15$ and $y \leq - 3 x - 5$ -10-10-5-55510100the overlap, cornered at $(- 4, 7)$
Graph $y \leq - x + 12$ and $y \leq 2 x - 3$ -10-10-5-55510100the overlap, cornered at $(5, 7)$
Graph $y > x + 8$ and $y \leq - x - 2$ -10-10-5-55510100the overlap, cornered at $(- 5, 3)$
Graph $y \geq 4 x - 6$ and $y > - x - 6$ -10-10-5-55510100the overlap, cornered at $(0, - 6)$
Graph $y < - x + 3$ and $y \leq - 3 x + 7$ -10-10-5-55510100the overlap, cornered at $(2, 1)$
Graph $y > - 4 x - 12$ and $y \geq 4 x + 20$ -10-10-5-55510100the overlap, cornered at $(- 4, 4)$
Graph $y \leq x + 6$ and $y > - 4 x - 9$ -10-10-5-55510100the overlap, cornered at $(- 3, 3)$
Graph $y \leq 2 x + 9$ and $y > 4 x + 19$ -10-10-5-55510100the overlap, cornered at $(- 5, - 1)$
Graph $y > - 4 x - 16$ and $y \geq x - 1$ -10-10-5-55510100the overlap, cornered at $(- 3, - 4)$
Graph $y < - 4 x - 12$ and $y \geq 2 x$ -10-10-5-55510100the overlap, cornered at $(- 2, - 4)$
Graph $y > - x + 8$ and $y \geq 3 x - 8$ -10-10-5-55510100the overlap, cornered at $(4, 4)$
Graph $y \leq - 3 x + 4$ and $y < - 4 x + 6$ -10-10-5-55510100the overlap, cornered at $(2, - 2)$
Graph $y > - 3 x - 13$ and $y < x + 11$ -10-10-5-55510100the overlap, cornered at $(- 6, 5)$
Graph $y < 2 x - 2$ and $y < - 4 x - 2$ -10-10-5-55510100the overlap, cornered at $(0, - 2)$
Graph $y \geq 2 x + 6$ and $y \leq x + 4$ -10-10-5-55510100the overlap, cornered at $(- 2, 2)$

How to do these

Graph $y \geq x - 1$ and $y < - 2 x + 4$

Shade above the first line, solid.
Shade below the second, dashed.
The solution is where both shadings land.

The answer is the overlap of the two regions.

Where students go wrong

Giving the whole shaded area rather than the overlap. Only the part covered by both counts, and it is easy to lose track once two greys sit on top of each other. Shading lightly, or with lines in two directions, keeps it readable.

Also called graphing systems of inequalities, feasible region or overlapping half planes.

Questions about these worksheets

Yes. Every systems of inequalities 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.

Precalculus is usually taken around 11th or 12th 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 systems of inequalities 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.

Precalculus systems of inequalities worksheet

Systems of Inequalities

Systems of InequalitiesAnswer keyVersion 1

How to do these

Where students go wrong

Questions about these worksheets

Are these systems of inequalities worksheets free?+

Do the systems of inequalities worksheets come with an answer key?+

Are these systems of inequalities worksheets printable?+

What grade are these systems of inequalities worksheets for?+

Can I get a different version of the same systems of inequalities worksheet?+

Is this a free alternative to Kuta Software for systems of inequalities?+

Can I choose how hard the systems of inequalities questions are?+

What do students get wrong with systems of inequalities?+