Class 9 Solutions of a Linear Equation — practice questions with answers
Linear Equations · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. A solution of a linear equation in two variables x and y is written as a pair (x, y). How many variables does such an equation contain?
A1
B2
C3
D0
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Answer: B) 2
A linear equation in two variables has exactly two variables, x and y, so a solution is a pair (x, y).
2. For x + y = 6, what is the value of x in the solution where y = 0 (the x-intercept)?
A6
B12
C7
D5
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Answer: A) 6
Put y = 0: x + 0 = 6, so x = 6. The solution is (6, 0).
3. A shopkeeper sells x kg of rice at Rs 40/kg and y kg of wheat at Rs 30/kg, earning exactly Rs 240. This is 40x + 30y = 240. If he sells 3 kg of rice, how many kg of wheat does he sell?
A3
B8
C4
D5
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Answer: C) 4
40(3) + 30y = 240, so 120 + 30y = 240, giving 30y = 120, y = 4 kg.
4. Lakshmi claims that (1, 1) is a solution of BOTH x + y = 2 and 2x - y = 1. Is her claim correct?
AYes, it satisfies both
BIt satisfies only the first
CIt satisfies only the second
DIt satisfies neither
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Answer: A) Yes, it satisfies both
x+y: 1+1=2 yes. 2x-y: 2-1=1 yes. (1,1) satisfies both equations.
5. A line of the form ax + by = 6 passes through the points (3, 0) and (0, 2). Using these, find the value of a.
A1
B4
C2
D3
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Answer: C) 2
Through (3,0): 3a = 6, so a = 2. (Check with (0,2): 2b = 6, b = 3; equation 2x + 3y = 6 fits both.)