8th Grade Systems of Linear Equations Worksheet (PDF)

8th Grade math worksheet: Systems of Linear Equations – Maths PDF

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This systems of equations worksheet for 8th Grade covers systems of linear equations (Common Core 8.EE.C.8a, 8.EE.C.8b, 8.EE.C.8c), with a free PDF to print.

These 21 problems practice systems of two linear equations solved by graphing, substitution and elimination (Common Core 8.EE.C.8a, 8.EE.C.8b and 8.EE.C.8c). Each problem has its own space for work, so print the page and write directly on it.

The problems start with direct skill checks and grow harder as you go. Later items include systems with no solution or infinitely many solutions and word problems. Use the answer key afterwards to check every step.

Grade 8 · Common Core State Standards: 8.EE.C.8a, 8.EE.C.8b, 8.EE.C.8c

Systems of equations worksheet: exercises 1 to 10

Exercise 1 – Check a solution

Is $(2, 3)$ a solution of $x + y = 5$ and $2x – y = 1$?

Exercise 2 – Not a solution

Is $(1, 2)$ a solution of $x + y = 3$ and $x – y = 2$?

Exercise 3 – Solve by graphing

A: y = 2x – 1 and B: y = -x + 5.

Read the solution of $y = 2x – 1$ and $y = -x + 5$ from the graph.

Exercise 4 – Graph two lines

Graph $y = 2x – 2$ and $y = -x + 4$ and find where they cross.

Exercise 5 – Substitution 1

Use substitution on $y = 2x$ and $x + y = 15$.

Exercise 6 – Substitution 2

Use substitution on $y = x + 3$ and $3x + y = 19$.

Exercise 7 – Substitution 3

Use substitution on $x = y – 2$ and $2x + 3y = 21$.

Exercise 8 – Elimination 1

Use elimination on $x + y = 16$ and $x – y = 6$.

Exercise 9 – Elimination 2

Use elimination on $3x + y = 17$ and $2x – y = 3$.

Exercise 10 – Elimination with a multiplier

Solve: $2x + 3y = 12$ and $x + y = 5$.

Exercises 11 and up

Exercise 11 – Elimination, opposite terms

Solve: $3x + 2y = 19$ and $5x – 2y = 5$.

Exercise 12 – Multiply both equations

Solve: $2x + 3y = 7$ and $3x + 2y = 8$.

Exercise 13 – Parallel lines

A: y = -3x + 2 and B: y = -3x + 7.

Decide how many solutions the system $y = -3x + 2$ and $y = -3x + 7$ has, and justify your answer.

Exercise 14 – Same line

Two equations, one line.

How many solutions does $2x + 2y = 8$ and $x + y = 4$ have?

Exercise 15 – Classify

Classify $3x – y = 4$ and $6x – 2y = 8$ as one, none or infinitely many solutions.

Exercise 16 – School play tickets

Prices for the school play.

Adult tickets cost \$12 and student tickets cost \$8. A school sold 50 tickets for \$480. How many of each kind were sold?

Exercise 17 – Bake sale

At a bake sale, muffins cost \$2 and cookies cost \$1.50. Ethan sold 40 items and collected \$65. How many muffins and cookies did he sell?

Exercise 18 – Gym plans

Total cost after x months.

Plan A costs \$25 to join plus \$10 per month. Plan B costs \$15 to join plus \$15 per month. After how many months do the plans cost the same? What is that cost?

Exercise 19 – Boat and current

Aisha’s boat travels 18 miles per hour downstream and 12 miles per hour upstream. Find the boat’s speed in still water and the speed of the current.

Exercise 20 – Coins

Priya has 30 coins, all dimes and quarters, worth \$4.50. How many dimes and how many quarters does she have?

Exercise 21 – Interpret the point

Two lines cross at $(4, 7)$. Explain what this point means for the system.

Key facts behind this systems of equations worksheet

Key facts

The solution of a system is the intersection point of the lines.
Different slopes: one solution. Same slope, different intercepts: no solution. Same line: infinitely many.
Substitution: solve one equation for a variable and substitute it into the other.
Elimination: add or subtract the equations to cancel a variable.
Always check the ordered pair in both equations.

How to use this systems of equations worksheet

Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.

Download the systems of equations worksheet as a PDF with the button below and keep it with your notes.

All Grade 8 chapters: Grade 8 math.

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