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Linear Equations in Two Variables — Class 9 CBSE Mathematics MCQs with Solutions
Free Class 9 CBSE Mathematics Linear Equations in Two Variables MCQs with step-by-step solutions. Practise online on Prepizo — no login needed.
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Sample questions with solutions
Q1 — easy
General standard form of a linear equation in two variables is:
A. ax + b = 0
B. ax + by + c = 0 ✓ Correct
C. ax² + by + c = 0
D. ax + by² = 0
Solution: Standard form is ax + by + c = 0 with a, b not both zero.
Q2 — easy
Number of solutions for a linear equation in two variables 2x + 3y = 6 is:
A. Unique solution
B. Two solutions
C. Infinitely many solutions ✓ Correct
D. No solution
Solution: A single linear equation in two variables has infinitely many solutions.
Q3 — easy
Graph of a linear equation in two variables ax + by + c = 0 is a:
A. Circle
B. Parabola
C. Straight line ✓ Correct
D. Hyperbola
Solution: Linear equations plot as straight lines on Cartesian plane.
Q4 — easy
Equation of x-axis is:
A. x = 0
B. y = 0 ✓ Correct
C. x = 1
D. y = 1
Solution: y = 0 defines x-axis.
Q5 — easy
Equation of y-axis is:
A. x = 0 ✓ Correct
B. y = 0
C. x + y = 0
D. x = y
Solution: x = 0 defines y-axis.
Q6 — easy
If (2, 0) is a solution of linear equation 2x + 3y = k, value of k is:
A. 4 ✓ Correct
B. 6
C. 5
D. 2
Solution: Substitute x = 2, y = 0: 2(2) + 3(0) = k → k = 4.
Q7 — easy
Any point on the line y = x is of the form:
A. (a, 0)
B. (0, a)
C. (a, a) ✓ Correct
D. (a, −a)
Solution: y = x implies both coordinates are equal: (a, a).
Q8 — easy
Line x = 5 is parallel to:
A. x-axis
B. y-axis ✓ Correct
C. Line y = x
D. Both axes
Solution: x = constant forms a line parallel to y-axis.
Q9 — easy
Line y = −3 is parallel to:
A. x-axis ✓ Correct
B. y-axis
C. Line y = x
D. Line y = −x
Solution: y = constant forms a line parallel to x-axis.
Q10 — easy
Cost of notebook is twice cost of pen. Linear equation representing statement is: (x = cost of notebook, y = cost of pen)
A. x − 2y = 0 ✓ Correct
B. 2x − y = 0
C. x + 2y = 0
D. x + y = 2
Solution: x = 2y → x − 2y = 0.
Q11 — easy
Which point lies on the line 3x + 2y = 12?
A. (2, 3)
B. (4, 0) ✓ Correct
C. (0, 4)
D. (1, 4)
Solution: Substitute (4,0): 3(4) + 2(0) = 12 (LHS = RHS).
Q12 — easy
Graph of equation x + y = 0 passes through:
A. Origin (0,0) ✓ Correct
B. (1,1)
C. (2,3)
D. (0,2)
Solution: 0 + 0 = 0, so line passes through origin.
Q13 — easy
If x = 1, y = 2 is a solution of equation 3x + 2ky = 7, then k =
A. 1 ✓ Correct
B. 2
C. 3
D. 4
Solution: 3(1) + 2k(2) = 7 → 3 + 4k = 7 → 4k = 4 → k = 1.
Q14 — easy
Line y = mx passes through:
A. Point (1,0)
B. Origin (0,0) ✓ Correct
C. Point (0,1)
D. Quadrant IV only
Solution: When x = 0, y = m(0) = 0 → passes through origin.
Q15 — easy
How many linear equations in x and y can be satisfied by x = 1 and y = 2?
A. Only 1
B. Only 2
C. Infinitely many ✓ Correct
D. None
Solution: Infinitely many lines can pass through a single point (1,2).