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Linear Equations in Two Variables Practice Questions

Class 9 · Mathematics · 2712 free MCQs with instant results and detailed explanations.

2712
Total
808
Easy
1397
Medium
507
Hard

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Topics in Linear Equations in Two Variables

Solution of Equations 949
Linear Equations 934
Graph of Linear Equation 829

Sample Questions from Linear Equations in Two Variables

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Q1
Easy
What is the general form of a linear equation in two variables?
A. Ax + By + C = 0
B. Ax^2 + By^2 = C
C. A + B = C
D. xy + C = 0
Show Answer & Explanation
Correct Answer: A
The general form of a linear equation in two variables is Ax + By + C = 0, where A, B, and C are constants.
Q2
Easy
What is the slope of the line represented by the equation 3x - 4y = 12?
A. -3/4
B. 4/3
C. 3/4
D. -4/3
Show Answer & Explanation
Correct Answer: A
Rearranging to slope-intercept form (y = mx + b) gives y = (3/4)x - 3, thus slope (m) = -3/4.
Q3
Easy
What is the graphical representation of the equation y = 4?
A. A vertical line
B. A horizontal line
C. A slanting line
D. A point
Show Answer & Explanation
Correct Answer: B
The equation y = 4 represents a horizontal line at y = 4 on the Cartesian plane.
Q4
Medium
The equation 5x - 2y = 10 represents which type of line in the Cartesian plane?
A. A vertical line
B. A horizontal line
C. A slanting line
D. A curve
Show Answer & Explanation
Correct Answer: C
The equation can be rearranged to y = (5/2)x - 5, which shows a slope, indicating a slanting line.
Q5
Medium
If 7x + 2y = 14 and 2x + y = 7, how many solutions does this system have?
A. One solution
B. No solution
C. Infinite solutions
D. Two solutions
Show Answer & Explanation
Correct Answer: C
Both equations represent the same line, resulting in infinite solutions.
Q6
Medium
Find the x-intercept of the line represented by the equation 6x + 3y = 18.
A. 2
B. 3
C. 4
D. 6
Show Answer & Explanation
Correct Answer: B
Setting y=0 in the equation gives 6x = 18, leading to x = 3 as the x-intercept.
Q7
Medium
How would you represent the equation 2y - 3x = 6 in slope-intercept form?
A. y = 3/2x + 3
B. y = 3/2x - 3
C. y = 3/2x + 6
D. y = 3x + 6
Show Answer & Explanation
Correct Answer: A
Rearranging gives y = (3/2)x + 3, which is in slope-intercept form.
Q8
Hard
The solution of the equation 2x + 3y = 6 is a pair of values (x, y). Which of the following pairs is a solution?
A. (0, 2)
B. (3, 0)
C. (1, 1)
D. (2, 0)
Show Answer & Explanation
Correct Answer: A
Plugging (0, 2) into the equation gives 2(0) + 3(2) = 6, which satisfies the equation.
Q9
Hard
The pair of equations 2x + 3y = 12 and 4x + 6y = 24 are which type?
A. Consistent and independent
B. Inconsistent
C. Dependent
D. Over-determined
Show Answer & Explanation
Correct Answer: C
Both equations represent the same line, hence they have infinitely many solutions, making them dependent.
Q10
Hard
Which of the following represents the equation of a line with a slope of -1 and y-intercept of 4?
A. y = -x + 4
B. y = 4x + 1
C. x + y = 4
D. y = -4x + 1
Show Answer & Explanation
Correct Answer: A
The slope-intercept form is y = mx + b. Here, m = -1 and b = 4.

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Linear Equations in Two Variables — Class 9 Mathematics Practice Questions Online

This page contains 2712 practice MCQs for the chapter Linear Equations in Two Variables in Class 9 Mathematics. The questions are organized by difficulty — 808 easy, 1397 medium, 507 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 3 topics, giving you comprehensive coverage of the entire chapter.