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.
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 \(y=-x+6\).
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 \(3x-y=8\).
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 \(2x-y=1\).
Problem 16: Parallel lines
How many solutions does the system \(y=2x+1\) and \(y=2x-3\) have? Explain using 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.
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.
See every chapter on the Grade 8 math page.