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Interactive practice · 14 questions on solving systems of equations by substitution — isolating a variable, substituting, back-solving, and the no-solution / infinitely-many special cases — with step-by-step solutions.
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Easy Solve by substitution: \(y = x + 1\) and \(x + y = 5\).
Answer: D — \((2,\,3)\)
Easy Solve by substitution: \(y = 3x\) and \(x + y = 8\).
Answer: A — \((2,\,6)\)
Medium Solve by substitution: \(y = 2x - 3\) and \(4x - y = 9\).
Answer: C — \((3,\,3)\)
Medium Solve by substitution: \(x = y + 2\) and \(2x + y = 10\).
Answer: B — \((4,\,2)\)
Medium Using substitution, solve \(y = x - 4\) and \(3x + 2y = 7\). What is \(x\)?
\(x=\)
Answer: 3
Medium Solve by substitution: \(y = -x + 6\) and \(2x - y = 3\).
Answer: D — \((3,\,3)\)
Hard Solve by substitution: \(x = 2y - 1\) and \(x + 3y = 9\).
Answer: B — \((3,\,2)\)
Medium When solving by substitution, the easiest variable to isolate first is one whose coefficient is:
Answer: C — \(1\) or \(-1\)
Medium Which system is set up most conveniently for substitution?
Answer: C — \(y = 3x - 2\) and \(x + y = 6\) (a variable is already isolated)
Hard Solve by substitution: \(y = 2x + 1\) and \(y = 2x - 3\).
Answer: D — no solution (parallel lines)
Hard Solve by substitution: \(y = 3x - 2\) and \(6x - 2y = 4\).
Answer: C — infinitely many solutions (same line)
Medium Using substitution, solve \(y = 4x\) and \(2x + y = 18\). What is \(y\)?
\(y=\)
Answer: 12
Medium Solve by substitution: \(x = 3y\) and \(x - y = 8\).
Answer: D — \((12,\,4)\)
Hard Solve by substitution: \(3x - y = 7\) and \(y = x + 1\).
Answer: B — \((4,\,5)\)