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Pair of Linear Equations in Two Variables Practice Questions

Class 10 · Mathematics · 1929 free MCQs with instant results and detailed explanations.

1929
Total
649
Easy
942
Medium
338
Hard

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Topics in Pair of Linear Equations in Two Variables

Cross-Multiplication Method 459
Graphical Method 662
Elimination Method 468
Substitution Method 340

Sample Questions from Pair of Linear Equations in Two Variables

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

Q1
Easy
What does the point of intersection of two linear equations represent in a graphical method?
A. The solution to the equations
B. The slope of the lines
C. The x-intercept of one line
D. The y-intercept of both lines
Show Answer & Explanation
Correct Answer: A
The point of intersection indicates the values of x and y that satisfy both equations simultaneously.
Q2
Easy
If the equations 2x + 3y = 6 and 4x + 6y = 12 are graphed, what can be said about their graphs?
A. They intersect at one point
B. They are parallel lines
C. They coincide
D. They form a right angle
Show Answer & Explanation
Correct Answer: C
The second equation is a multiple of the first, meaning they represent the same line and hence coincide.
Q3
Easy
Which of the following pairs of equations will yield a unique solution when graphed?
A. x + y = 5 and x + y = 10
B. 2x - y = 3 and 4x - 2y = 6
C. x - y = 1 and 2x + y = 4
D. 3x + 3y = 9 and 6x + 6y = 18
Show Answer & Explanation
Correct Answer: C
Equations in option C are independent, leading to a unique intersection point.
Q4
Medium
What is the point of intersection of the lines represented by the equations 2x + 3y = 6 and x - y = 1?
A. (1, 1)
B. (2, 0)
C. (0, 2)
D. (3, -2)
Show Answer & Explanation
Correct Answer: A
The point (1,1) satisfies both equations when substituted back, confirming it's the intersection point.
Q5
Medium
Which of the following pairs of equations represents parallel lines?
A. 2x + 4y = 12 and x + 2y = 6
B. 3x - 2y = 6 and 6x - 4y = 12
C. x + y = 1 and x + y = 2
D. 2x - y = 3 and -2x + y = 5
Show Answer & Explanation
Correct Answer: B
Equations B have the same coefficients for x and y, indicating parallel lines with no intersection.
Q6
Medium
If the equations x + 2y = 4 and 2x + 4y = 8 are plotted on a graph, what type of lines do they represent?
A. Intersecting
B. Parallel
C. Coinciding
D. None of the above
Show Answer & Explanation
Correct Answer: C
Both equations represent the same line, thus they are coinciding lines.
Q7
Medium
What is the solution set of the equations y = 2x + 3 and y = -x + 1?
A. All real numbers
B. No solutions
C. {(-1, 1)}
D. One unique point
Show Answer & Explanation
Correct Answer: D
The two lines intersect at exactly one point; hence there is a unique solution.
Q8
Hard
If the pair of equations 2x + 3y = 6 and 4x + 6y = 12 are graphically represented, what is the nature of the lines?
A. The lines intersect at one point.
B. The lines are parallel.
C. The lines coincide.
D. The lines are perpendicular.
Show Answer & Explanation
Correct Answer: C
Both equations represent the same line, hence they coincide.
Q9
Hard
The lines represented by the equations x + 2y = 4 and 2x + 4y = 8 are represented graphically. How many solutions do they have?
A. No solution
B. One solution
C. Infinite solutions
D. Two solutions
Show Answer & Explanation
Correct Answer: C
The second equation is a multiple of the first, indicating infinite solutions.
Q10
Hard
Consider the equations 3x + 2y = 12 and x - y = 1. How would you graphically find the solution?
A. Find the x-intercepts only.
B. Graph both lines and find their intersection.
C. Solve for y in both equations.
D. Determine the slopes of both lines.
Show Answer & Explanation
Correct Answer: B
Graphing both lines and finding their intersection will give the solution to the equations.

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Pair of Linear Equations in Two Variables — Class 10 Mathematics Practice Questions Online

This page contains 1929 practice MCQs for the chapter Pair of Linear Equations in Two Variables in Class 10 Mathematics. The questions are organized by difficulty — 649 easy, 942 medium, 338 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 4 topics, giving you comprehensive coverage of the entire chapter.