Class 10 Elimination 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 elimination method, what is the first goal when solving a pair of linear equations?
AMake the coefficient of one variable equal (in magnitude) in both equations
BMake the constant terms equal
CSquare both equations
DFind the y-intercept of each line
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Answer: A) Make the coefficient of one variable equal (in magnitude) in both equations
Elimination works by adding or subtracting the equations so that one variable cancels; this requires its coefficients to be equal in magnitude first.
2. Solve by elimination: 2x + 3y = 13 and 2x - y = 1. Find y.
A2
B3
C4
D6
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Answer: B) 3
Subtract second from first: 4y = 12, so y = 3.
3. Solve by elimination: 5x + 4y = 22 and 3x + 4y = 18. Find x.
A1
B2
C3
D4
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Answer: B) 2
Subtract second from first: 2x = 4, so x = 2.
4. The present ages of a father and son add up to 65 years. Five years ago, the father was 4 times as old as the son, giving F - 4S = -15. Using elimination on F + S = 65 and F - 4S = -15, find the son's present age (in years).
A16
B13
C20
D15
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Answer: A) 16
Subtract second from first: 5S = 80, so S = 16 years. (Then F = 49; five years ago 44 = 4 x 11.)
5. A farmer in Punjab has hens and goats. Counting heads gives 40, and counting legs gives 116. If h = number of hens and g = number of goats, then h + g = 40 (heads) and 2h + 4g = 116 (legs). Using elimination, find the number of goats.
A17
B18
C36
D19
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Answer: B) 18
Multiply heads equation by 2: 2h + 2g = 80. Subtract from legs equation: 2g = 36, so g = 18 goats (and 22 hens).