Kerala SSLC · Mathematics · Class 10

Pairs of Equations: Important Questions with Answers

These are 10 important multiple-choice questions from the Kerala SSLC Mathematics chapter “Pairs of Equations” (Kerala SCERT syllabus). Each one shows the correct answer and a short explanation of why it is right. Try answering before you read the answer. ExamSummary has 20 practice questions on this chapter in total.

1. Q1.If a system of linear equations has no solution, the lines representing them on a graph are:

   • A)Intersecting
   • B)Coincident
   • C)Parallel
   • D)Perpendicular

   Answer: C) Parallel

   No solution implies there is no common point between the lines. Geometrically, this occurs when the lines are parallel, meaning they have the same slope but different intercepts.

2. Q2.Five pens and six pencils cost ₹50. Three pens and four pencils cost ₹30. If the cost of a pen is p and pencil is q, the system of equations is:

   • A)5p + 6q = 50, 3p + 4q = 30
   • B)5p + 6q = 30, 3p + 4q = 50
   • C)5p - 6q = 50, 3p - 4q = 30
   • D)6p + 5q = 50, 4p + 3q = 30

   Answer: A) 5p + 6q = 50, 3p + 4q = 30

   Direct translation of the word problem yields 5 times pen cost plus 6 times pencil cost equals total cost for the first case, and similarly for the second case.

3. Q3.For the pair of linear equations 2x + 3y = 7 and (k+1)x + (2k-1)y = 4k+1 to have infinitely many solutions, what is the value of k?

   • A)4
   • B)5
   • C)6
   • D)3

   Answer: B) 5

   For infinitely many solutions, the ratios of coefficients must be equal: a1/a2 = b1/b2 = c1/c2. Solving 2/(k+1) = 3/(2k-1) gives k=5, which also satisfies the constant term ratio 7/(4k+1) = 1/3.

4. Q4.If the lines represented by the equations ax + by = c and dx + ey = f intersect at exactly one point, which condition must hold true?

   • A)a/d = b/e
   • B)a/d ≠ b/e
   • C)a/d = c/f
   • D)b/e = c/f

   Answer: B) a/d ≠ b/e

   A unique solution exists when the lines are intersecting, which implies their slopes are different. Therefore, the ratio of the coefficients of x must not equal the ratio of the coefficients of y (a/d ≠ b/e).

5. Q5.Solve the system of equations: x + y = 14 and x - y = 4. What are the values of x and y?

   • A)(9, 5)
   • B)(5, 9)
   • C)(10, 4)
   • D)(4, 10)

   Answer: A) (9, 5)

   Adding the two equations eliminates y, giving 2x = 18 or x = 9. Substituting x=9 into the first equation yields 9 + y = 14, so y = 5. Thus, the solution is (9, 5).

6. Q6.Five pens and three pencils cost ₹30. Three pens and five pencils cost ₹26. What is the cost of one pen?

   • A)₹4
   • B)₹4.5
   • C)₹5
   • D)₹3.5

   Answer: B) ₹4.5

   Let cost of pen be p and pencil be q. Solving 5p + 3q = 30 and 3p + 5q = 26 using elimination gives p = 4.5 and q = 2.5. Therefore, one pen costs ₹4.5.

7. Q7.To solve the non-linear equations (1)/(x) + (1)/(y) = 2 and (1)/(x) - (1)/(y) = 0, which substitution makes them linear?

   • A)u = x, v = y
   • B)u = 1/x, v = 1/y
   • C)u = x², v = y²
   • D)u = xy, v = x+y

   Answer: B) u = 1/x, v = 1/y

   By substituting u = 1/x and v = 1/y, the equations become u + v = 2 and u - v = 0, which are linear equations in terms of u and v and can be solved easily.

8. Q8.The pair of equations x + 2y - 3 = 0 and 2x + 4y - 6 = 0 represents:

   • A)Intersecting lines
   • B)Parallel lines
   • C)Coincident lines
   • D)Perpendicular lines

   Answer: C) Coincident lines

   Comparing ratios a1/a2 = 1/2, b1/b2 = 2/4 = 1/2, and c1/c2 = -3/-6 = 1/2. Since all ratios are equal, the lines are coincident (representing the same line).

9. Q9.If x = a and y = b is the solution of x - y = 2 and x + y = 4, what is the value of a + b?

   • A)2
   • B)3
   • C)4
   • D)5

   Answer: C) 4

   Solving the system gives x=3 and y=1, so a=3 and b=1. Adding these values results in a + b = 3 + 1 = 4.

10. Q10.For the equations 3x + 2y = 12 and 2x + 3y = 13, what is the value of x?

    • A)1
    • B)2
    • C)3
    • D)4

    Answer: B) 2

    Using the elimination method, multiply the first equation by 3 and the second by 2 to get 9x + 6y = 36 and 4x + 6y = 26. Subtracting them gives 5x = 10, so x = 2.

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