Difficulty
Calculator
Interactive practice · 14 questions on solving systems of equations by elimination — adding/subtracting, multiplying to match coefficients, and the no-solution / infinitely-many special cases — with step-by-step solutions.
Press Check answer on each question to see whether you got it right — every check is timestamped and recorded in your Activity log below.
Each attempt is saved under its own name — load, rename, or delete them below. Difficulty / calculator tags are shared across all attempts. Numeric answers accept equivalent forms (e.g. 4/3 or 1.333).
The timer is stopped. Questions are hidden until you resume.
Easy Solve by elimination: \(x + y = 7\) and \(x - y = 1\).
Answer: D — \((4,\,3)\)
Easy Solve by elimination: \(2x + y = 9\) and \(x - y = 3\).
Answer: A — \((4,\,1)\)
Medium Solve by elimination: \(4x + y = 14\) and \(2x + y = 8\).
Answer: C — \((3,\,2)\)
Medium Solve by elimination: \(3x + 4y = 10\) and \(3x + 2y = 8\).
Answer: B — \((2,\,1)\)
Medium Solve by elimination (multiply one equation first): \(x + 2y = 7\) and \(3x - y = 7\).
Answer: C — \((3,\,2)\)
Hard Solve by elimination: \(2x + 3y = 7\) and \(3x + 2y = 8\).
Answer: D — \((2,\,1)\)
Medium Using elimination, solve \(x + y = 10\) and \(x - y = 4\). What is \(x\)?
\(x=\)
Answer: 7
Medium The elimination method works by adding or subtracting the equations in order to:
Answer: C — cancel (eliminate) one of the variables
Medium To eliminate a variable by adding the equations, its two coefficients must be:
Answer: C — opposites (e.g. \(+3y\) and \(-3y\))
Hard To eliminate \(x\) from \(2x + 3y = 12\) and \(5x - 2y = 1\) by adding, multiply the equations by:
Answer: D — \(5\) and \(-2\) (to make \(+10x\) and \(-10x\))
Hard Solve by elimination: \(2x + y = 5\) and \(4x + 2y = 12\).
Answer: C — no solution (parallel lines)
Hard Solve by elimination: \(x - 3y = 4\) and \(2x - 6y = 8\).
Answer: B — infinitely many solutions (same line)
Medium Solve by elimination: \(5x + 2y = 16\) and \(3x + 2y = 12\).
Answer: D — \((2,\,3)\)
Hard Solve by elimination: \(4x - 3y = 5\) and \(2x + y = 5\).
Answer: B — \((2,\,1)\)