CBSE Class 10 Â· Mathematics Â· Chapter 3

Class 10 Maths â€“ Pair of Linear Equations Quiz

Answer 20 multiple-choice questions on pairs of linear equations in two variables, including 14 verified CBSE previous year questions. Each question is worth 1 mark and you get 20 minutes.

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This quiz is timed. You have 20 minutes to answer all 20 questions. Warnings appear at the 5, 2 and 1 minute marks, and the quiz submits automatically when time runs out.

About the questions

Questions labelled CBSE PYQ are from actual CBSE board papers and the year of the board exam is shown. Questions labelled Original Â· CBSE Exam-Style are original items written by Vyasa Academy in the board pattern. All questions stay within the pair-of-linear-equations-in-two-variables scope of this chapter.

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Question 1Moderate

If \(x = 1\) and \(y = 2\) is a solution of the pair of linear equations \(2x - 3y + a = 0\) and \(2x + 3y - b = 0\), then:

A\(a = 2b\) B\(2a = b\) C\(a + 2b = 0\) D\(2a + b = 0\)

Question 2Moderate

For which value of \(p\) will the pair of linear equations \(px + 3y = p - 3\) and \(12x + py = p\) have infinitely many solutions?

A\(p = 6\) B\(p = -6\) C\(p = \pm 6\) D\(p = 3\)

Question 3Easy

The line represented by the equation \(x - y = 0\) is:

Fig.: The line \(x - y = 0\) passes through the origin.

Aparallel to the \(x\)-axis Bparallel to the \(y\)-axis Cpassing through the origin Dpassing through the point \((3, 2)\)

Question 4Easy

The equation of a line parallel to the \(x\)-axis and at a distance of 3 units below the x-axis is:

A\(x = 3\) B\(y = -3\) C\(x = -3\) D\(y = 3\)

Question 5Easy

A system of two linear equations in two variables is inconsistent, if the lines in the graph are:

Aintersecting at one point Bintersecting at right angles Cparallel Dcoincident

Question 6Challenging

The system of equations \(2x + 1 = 0\) and \(8y - 5 = 0\) has:

Fig.: \(2x + 1 = 0\) is the vertical line \(x = -\frac{1}{2}\) and \(8y - 5 = 0\) is the horizontal line \(y = \frac{5}{8}\).

Aa unique solution Btwo solutions Cno solution Dan infinite number of solutions

Question 7Challenging

The system of equations \(x + 5 = 0\) and \(2x - 1 = 0\) has:

Fig.: \(x + 5 = 0\) and \(2x - 1 = 0\) give two parallel vertical lines.

Aunique solution Bno solution Ctwo solutions Dinfinite solutions

Question 8Moderate

The value of \(k\) for which the pair of linear equations \(x + y - 4 = 0\) and \(2x + ky - 8 = 0\) has infinitely many solutions is:

A\(k = 2\) B\(k = 4\) C\(k = 6\) D\(k = 1\)

Question 9Moderate

The pair of linear equations \(y + a = 0\) and \(2x = b\), where \(a\) and \(b\) are non-zero constants, has the solution:

A\((\frac{b}{2}, a)\) B\((b, -\frac{a}{2})\) C\((\frac{b}{2}, -a)\) D\((-\frac{b}{2}, -a)\)

Question 10Moderate

The straight lines represented by the system of equations \(3x + 4y = 5\) and \(6x + 8y = 7\) are:

Aintersecting at a point Bparallel Ccoincident Dintersecting at the point \((1, 2)\)

Question 11Easy

If a pair of linear equations in two variables is represented by two coincident lines, then the pair of equations has:

Aone solution Btwo solutions Cno solution Dinfinitely many solutions

Question 12Moderate

In the given figure, graphs of two linear equations are shown. The pair of these linear equations is:

Fig.: The graphs of the two equations intersect at exactly one point.

Ainconsistent Bconsistent with infinitely many solutions Cconsistent with a unique solution Dinconsistent but can be made consistent by extending these lines

Question 13Moderate

The solution of the system of linear equations \(7x - 2y = 5\) and \(8x + 7y = 15\) is:

A\((3, 2)\) B\((-1, 1)\) C\((1, 1)\) D\((2, 3)\)

Question 14Challenging

Tara scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each wrong answer, then Tara would have scored 50 marks. Assuming that Tara attempted all questions, the total number of questions in the test is:

A12 B15 C18 D20

Question 15Moderate

Using the substitution method, the solution of the pair of equations \(x + y = 5\) and \(x - y = 1\) is:

A\((2, 3)\) B\((5, 0)\) C\((-3, 2)\) D\((3, 2)\)

Question 16Moderate

3 pens and 5 pencils together cost ₹19, while 4 pens and 2 pencils together cost ₹16. The cost of one pencil is:

A₹3 B₹4 C₹1 D₹2

Question 17Moderate

The present age of a father is three times the present age of his son. If the sum of their present ages is 40 years, then the age of the son is:

A10 years B12 years C15 years D8 years

Question 18Challenging

Rohan claims that the point \((2, 3)\) is a solution of the pair of linear equations \(x + 2y = 8\) and \(2x - y = 5\). Which of these statements is correct?

ARohan is correct; \((2, 3)\) satisfies both equations B\((2, 3)\) satisfies neither equation C\((2, 3)\) satisfies only the first equation D\((2, 3)\) satisfies only the second equation

Question 19Challenging

2 adult and 3 child movie tickets together cost ₹700, while 3 adult and 2 child movie tickets together cost ₹800. If an adult ticket costs \(x\) rupees and a child ticket costs \(y\) rupees, the pair of linear equations representing this situation is:

A\(2x + 3y = 700\), \(3x + 2y = 800\) B\(3x + 2y = 700\), \(2x + 3y = 800\) C\(2x + 3y = 800\), \(3x + 2y = 700\) D\(2x - 3y = 700\), \(3x - 2y = 800\)

Question 20Challenging

To decide the nature of the pair of linear equations \(x + 2y = 5\) and \(2x + 4y = 9\) without graphing them, we compare the ratios of the coefficients. Which conclusion holds?

A\(\frac{a_1}{a_2} \neq \frac{b_1}{b_2}\), so the lines intersect at exactly one point B\(\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}\), so the lines coincide C\(\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}\), so the lines are parallel D\(\frac{a_1}{a_2} \neq \frac{b_1}{b_2}\), so the lines are parallel

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