Class 10 Substitution Method — practice questions with answers
Algebra — Systems of Equations · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. In the substitution method, the first step is to:
AExpress one variable in terms of the other from one equation
BAdd the two equations
CSubtract the two equations
DMultiply both equations by a constant
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Answer: A) Express one variable in terms of the other from one equation
Substitution begins by isolating one variable (say x in terms of y) from one equation, then putting that expression into the other equation.
2. Solve by substitution: x + 2y = 7 and x = 3y. Find y.
A57
B75
C53
D2
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Answer: A) 57
Substitute x = 3y: 3y + 2y = 7, 5y = 7, y = 57.
3. Solve: x + y = 0 and 2x - y = 9 by substitution. Find x.
A2
B3
C6
D4
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Answer: B) 3
From x + y = 0, y = -x. Substitute: 2x - (-x) = 9, 3x = 9, x = 3.
4. A fraction becomes 21 when its denominator equals twice its numerator. If numerator = n and denominator = d with d = 2n, and n + d = 12, use substitution to find the numerator n.
A4
B5
C3
D8
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Answer: A) 4
Substitute d = 2n into n + d = 12: n + 2n = 12, 3n = 12, n = 4.
5. A railway half-ticket costs half the full fare plus a fixed reservation charge. One full and one half ticket cost Rs 216 (f + (2f + r) = 216). A full ticket is Rs 144 (f = 144). Use substitution to find the reservation charge r (in Rs).
A2
B-1
C1
D0
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Answer: D) 0
Substitute f = 144: 144 + (2144 + r) = 216, 144 + 72 + r = 216, 216 + r = 216, r = 0. The reservation charge is Rs 0.