This grade 8 systems of equations worksheet gives 24 problems on systems of linear equations, ordered from easy to hard, with a separate answer key.
These problems practice Common Core standards 8.EE.C.8a, 8.EE.C.8b and 8.EE.C.8c. Check ordered pairs, read solutions from graphs, and solve systems by graphing, substitution and elimination. Then decide when a system has no solution or infinitely many.
The last six problems are word problems: write two equations, solve them, and check the answer in the story. Problems run from easiest to hardest.
Grade 8 Systems of Equations Worksheet: problems 1–5
Problem 1: Is it a solution?
Determine whether \((2,3)\) is a solution of the system \(y=2x-1\) and \(y=-x+5\).
Problem 2: Test an ordered pair
Determine whether \((4,1)\) is a solution of \(x+y=5\) and \(x-y=2\).
Problem 3: Read the intersection
The graph shows \(y=x-1\) and \(y=-2x+5\). Find the solution of the system from the graph, then check it in both equations.
Problem 4: Solve by graphing
Solve the system by graphing: \(y=x+2\) and \(y=-x+4\).
Problem 5: Graph two lines
Solve the system by graphing: \(y=2x\) and \(y=-x+6\).
Grade 8 Systems of Equations Worksheet: problems 6–10
Problem 6: Standard form on a grid
Solve the system by graphing: \(x+y=6\) and \(x-y=2\).
Problem 7: Substitute a product
Solve by substitution: \(y=3x\) and \(x+y=12\).
Problem 8: Substitute a sum
Solve by substitution: \(y=x+4\) and \(2x+y=13\).
Problem 9: Two expressions for y
Solve the system: \(y=2x-3\) and \(y=x+2\).
Problem 10: Substitute for x
Solve by substitution: \(x=2y+1\) and \(3x-y=8\).
Grade 8 Systems of Equations Worksheet: problems 11–15
Problem 11: Add the equations
Solve by elimination: \(x+y=10\) and \(x-y=4\).
Problem 12: Opposite coefficients
Solve by elimination: \(2x+y=11\) and \(3x-y=9\).
Problem 13: Eliminate y
Solve by elimination: \(3x+2y=19\) and \(x-2y=1\).
Problem 14: Multiply one equation
Solve by elimination: \(2x+3y=13\) and \(x+y=5\).
Problem 15: Make y cancel
Solve by elimination: \(3x+2y=12\) and \(2x-y=1\).
Grade 8 Systems of Equations Worksheet: problems 16–20
Problem 16: Parallel lines
Decide how many solutions the system \(y=-x+4\) and \(y=-x-1\) has. Justify the answer with the graph.
Problem 17: No solution by inspection
Without graphing, explain why \(3x+2y=5\) and \(3x+2y=6\) have no solution.
Problem 18: Same line twice
How many solutions does the system \(y=3x-2\) and \(6x-2y=4\) have?
Problem 19: Movie tickets
Adult tickets cost $9 and child tickets cost $6. Mei buys 8 tickets for $57. Write a system and find how many adult and child tickets she bought.
Problem 20: Saving money
Maya has $20 and saves $5 each week. Jamal has $50 and saves $2 each week. The graph shows both. Write a system, then find when they have the same amount and how much that is.
Grade 8 Systems of Equations Worksheet: problems 21–24
Problem 21: Phone plans
Plan A costs $20 a month plus $0.10 per minute. Plan B costs $10 a month plus $0.20 per minute. For how many minutes is the monthly cost the same, and what is that cost?
Problem 22: Bake sale
At a bake sale, muffins cost $3 and cookies cost $2. Ethan sold 30 items and collected $70. How many muffins and cookies did he sell?
Problem 23: Coins in a jar
Priya has 15 coins, all nickels and dimes, worth $1.20 (120 cents). How many nickels and how many dimes does she have?
Problem 24: Two numbers
The sum of two numbers is 24 and their difference is 6. Find the numbers.
How to use this grade 8 systems of equations worksheet
Print this grade 8 systems of equations worksheet as a PDF, solve every problem on paper, then compare with the answer key.
See every chapter on the Grade 8 math page.