Class 10 Mathematics Part 1 (Algebra) – Chapter 1: Linear Equations in Two Variables MCQ

10 questions · this chapter only · Balbharati textbook

Timed quiz: 15 seconds per question, score at the end. Or solve without the timer: tap an option, right turns green, wrong turns red.

1. For the equations 2x + 3y = 8 and 4x − y = 2, what is the value of the determinant D?

   Chapter 1: Linear Equations in Two Variables

   • A−14
   • B14
   • C−10
   • D10
   Show answer

   Answer: A. −14
   D = a₁b₂ − a₂b₁ = (2)(−1) − (4)(3) = −2 − 12 = −14.

2. What is the solution of the simultaneous equations x + y = 7 and x − y = 1?

   Chapter 1: Linear Equations in Two Variables

   • A(x, y) = (3, 4)
   • B(x, y) = (4, 3)
   • C(x, y) = (5, 2)
   • D(x, y) = (2, 5)
   Show answer

   Answer: B. (x, y) = (4, 3)
   Adding gives 2x = 8, so x = 4; then y = 7 − 4 = 3.

3. The graph of the equation y = 3 (that is, 0x + y = 3) is a line that is:

   Chapter 1: Linear Equations in Two Variables

   • AParallel to the Y-axis
   • BPassing through the origin
   • CParallel to the X-axis
   • DThe Y-axis itself
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   Answer: C. Parallel to the X-axis
   For every x, y stays 3, so all points lie on a line parallel to the X-axis.

4. When two simultaneous equations are solved by the graphical method, the solution is given by:

   Chapter 1: Linear Equations in Two Variables

   • AThe point where the first line meets the X-axis
   • BThe point where the second line meets the Y-axis
   • CThe origin
   • DThe coordinates of the point where the two lines intersect
   Show answer

   Answer: D. The coordinates of the point where the two lines intersect
   The intersection point lies on both lines, so its coordinates satisfy both equations.

5. In Cramer's method, the value of x is found by which formula?

   Chapter 1: Linear Equations in Two Variables

   • Ax = Dx / D
   • Bx = D / Dx
   • Cx = Dy / D
   • Dx = D / Dy
   Show answer

   Answer: A. x = Dx / D
   Cramer's rule: x = Dx/D and y = Dy/D, with D ≠ 0.

6. Solve 23x + 27y = 73 and 27x + 23y = 77.

   Chapter 1: Linear Equations in Two Variables

   • A(x, y) = (1, 2)
   • B(x, y) = (3, 0)
   • C(x, y) = (2, 1)
   • D(x, y) = (2, 3)
   Show answer

   Answer: C. (x, y) = (2, 1)
   Adding: 50x + 50y = 150 so x + y = 3; subtracting: 4x − 4y = 4 so x − y = 1; hence x = 2, y = 1.

7. How many solutions do the equations x + 3y = 5 and 2x + 6y = 10 have?

   Chapter 1: Linear Equations in Two Variables

   • ANo solution
   • BExactly one
   • CExactly two
   • DInfinitely many
   Show answer

   Answer: D. Infinitely many
   The second equation is 2 times the first, so both graphs are the same line and every point on it is a solution.

8. The determinant method of solving simultaneous equations was first given by which Swiss mathematician?

   Chapter 1: Linear Equations in Two Variables

   • ALeonhard Euler
   • BGabriel Cramer
   • CJakob Bernoulli
   • DJohann Bernoulli
   Show answer

   Answer: B. Gabriel Cramer
   The method was first given by Gabriel Cramer of Geneva, so it is called Cramer's method.

9. By putting 1/x = m and 1/y = n, solve 1/x + 1/y = 5 and 1/x − 1/y = 1.

   Chapter 1: Linear Equations in Two Variables

   • A(x, y) = (3, 2)
   • B(x, y) = (1/3, 1/2)
   • C(x, y) = (1/2, 1/3)
   • D(x, y) = (2, 3)
   Show answer

   Answer: B. (x, y) = (1/3, 1/2)
   m + n = 5 and m − n = 1 give m = 3, n = 2, so x = 1/m = 1/3 and y = 1/n = 1/2.

10. The sum of two numbers is 25 and their difference is 7. What are the numbers?

    Chapter 1: Linear Equations in Two Variables

    • A16 and 9
    • B18 and 7
    • C15 and 10
    • D17 and 8
    Show answer

    Answer: A. 16 and 9
    x + y = 25 and x − y = 7 give 2x = 32, so x = 16 and y = 9.

All questions are written by PadhaiNotes in our own words from this chapter of the official Maharashtra State Board Balbharati textbook.