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Karnataka SSLC (Class 10) Pair of Linear Equations in Two Variables — practice questions

Explore 11 free Pair of Linear Equations in Two Variables questions in Karnataka SSLC (Class 10) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Pair of Linear Equations in Two Variables questions and exercises with answers

Showing questions 1–11 of 11.

If the two lines represented by a pair of linear equations intersect at a single point, the pair hasRead the answer and worked solution →If the two lines of a pair of linear equations are parallel, the pair hasRead the answer and worked solution →If the two lines of a pair of linear equations are coincident (same line), the pair hasRead the answer and worked solution →A pair of linear equations that has at least one solution is said to beRead the answer and worked solution →The pair of equations $2x+3y=5$ and $4x+6y=10$ hasRead the answer and worked solution →The pair of equations $x+2y=4$ and $2x+4y=12$ hasRead the answer and worked solution →Solving $x+y=14$ and $x-y=4$ givesRead the answer and worked solution →Which of these is NOT an algebraic method of solving a pair of linear equations?Read the answer and worked solution →For what value of $k$ do the equations $2x+3y=7$ and $6x+9y=k$ have infinitely many solutions?Read the answer and worked solution →The sum of two numbers is 20 and their difference is 6. The larger number isRead the answer and worked solution →If a pair of linear equations is inconsistent, the graph of the two equations will beRead the answer and worked solution →

Worked practice questions

If the two lines represented by a pair of linear equations intersect at a single point, the pair has

  1. a unique solution
  2. no solution
  3. infinitely many solutions
  4. exactly two solutions
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Correct answer: A. a unique solution

1. The solution of a pair of linear equations is the point(s) common to both lines. 2. Two lines that intersect meet at exactly one point, giving **a unique solution**. 3. Such a pair is consistent. _Source: Karnataka SSLC (KSEEB) Class 10 Mathematics, Ch3 'Pair of Linear Equations in Two Variables', §3.2_

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If the two lines of a pair of linear equations are parallel, the pair has

  1. a unique solution
  2. no solution
  3. infinitely many solutions
  4. one solution
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Correct answer: B. no solution

1. Parallel lines never meet, so there is no common point. 2. Hence the pair has **no solution** and is called inconsistent. 3. Their coefficients satisfy a₁/a₂ = b₁/b₂ ≠ c₁/c₂. _Source: Karnataka SSLC (KSEEB) Class 10 Mathematics, Ch3 'Pair of Linear Equations in Two Variables', §3.2_

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If the two lines of a pair of linear equations are coincident (same line), the pair has

  1. no solution
  2. a unique solution
  3. infinitely many solutions
  4. two solutions
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Correct answer: C. infinitely many solutions

1. Coincident lines lie exactly on top of each other. 2. Every point on the line satisfies both equations, so there are **infinitely many solutions**. 3. Their coefficients satisfy a₁/a₂ = b₁/b₂ = c₁/c₂. _Source: Karnataka SSLC (KSEEB) Class 10 Mathematics, Ch3 'Pair of Linear Equations in Two Variables', §3.2_

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