8th Grade Math · Systems of Equations
Standard form Worksheets
Fresh practice, ready to print. Answer key included.
Pairs such as 2x + y = 7 and x − y = 2. Add or subtract to eliminate a variable.
Make it yours
Or start with a ready-made version.
How it works: a quick refresher
The rules this worksheet practices, then one problem worked from start to finish.
| Strategy | How it works |
|---|---|
| A solution makes both equations true | The pair (x, y) has to work in the first equation and in the second. |
| Substitution sets the expressions equal | If y = 2x + 1 and y = −x + 7, then 2x + 1 = −x + 7. |
| Elimination matches a column | In 2x + y = 7 and x − y = 2, adding removes y because +y and −y cancel. |
| Same slope, different intercept: no solution | y = 2x + 1 and y = 2x + 5 never meet. Parallel lines do not share a point. |
| Same line: infinitely many solutions | y = 2x + 1 and 2y = 4x + 2 are the same line written two ways. Every point on the line works. |
Worked example
Solve y = 2x + 1, y = −x + 7.
- 1Set the right sides equal: 2x + 1 = −x + 7.
- 2Add x to both sides: 3x + 1 = 7. Then 3x = 6, so x = 2.
- 3y = 2(2) + 1 = 5. The pair is (2, 5).
- 4Check the other equation: −(2) + 7 = 5.
Ready-made versions
Three fixed versions you can link to or share. Each is a PDF with its own answer key.
- Standard form Worksheets, version 1Worksheet PDFAnswer key PDF
- Standard form Worksheets, version 2Worksheet PDFAnswer key PDF
- Standard form Worksheets, version 3Worksheet PDFAnswer key PDF
Grade level and standard
Written for 8th grade math (expressions and equations) and aligned to CCSS 8.EE.C.8. It also works as review in later grades.
Common questions
- Is there an answer key?
- Yes. Every worksheet has a matching answer key with each answer worked on the same grid or layout as the question. The worksheet code printed at the bottom of each page pairs a sheet with its key.
- What does no solution mean?
- The two equations describe parallel lines that are not the same line. No pair (x, y) makes both true. Write no solution, not a pair.
- What does infinitely many solutions mean?
- The two equations are the same line, sometimes with both sides multiplied by the same number. Every point on that line is a solution. Write infinitely many solutions, not one example pair.
- How many different versions are there?
- About a million per skill. Each time you press the button the problems are generated fresh, so you can print a different version for every student, a retake, or another night of practice.
- Are the worksheets free?
- Yes. They are free to print and copy for your home or classroom, with no sign-up.
Was this worksheet helpful?
Tell us what worked or what didn't. Need a different skill? Request a worksheet.