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Maharashtra SSC (Class 10) Linear Equations in Two Variables — practice questions

Explore 9 free Linear Equations in Two Variables questions in Maharashtra SSC (Class 10) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Linear Equations in Two Variables questions and exercises with answers

Showing questions 1–9 of 9.

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 →How many solutions does the pair have?Read the answer and worked solution →Which one does NOT belong?Read the answer and worked solution →

Worked practice questions

The pair of equations $2x+3y=5$ and $4x+6y=10$ has

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

1. Compare ratios: $\dfrac{a_1}{a_2}=\dfrac{2}{4}=\dfrac12$, $\dfrac{b_1}{b_2}=\dfrac{3}{6}=\dfrac12$, $\dfrac{c_1}{c_2}=\dfrac{5}{10}=\dfrac12$. 2. All three ratios are equal, so the lines are coincident. 3. Hence there are **infinitely many solutions**. _Source: Karnataka SSLC (KSEEB) Class 10 Mathematics, Ch3 'Pair of Linear Equations in Two Variables', §3.2_

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The pair of equations $x+2y=4$ and $2x+4y=12$ has

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

1. Ratios: $\dfrac{a_1}{a_2}=\dfrac12$, $\dfrac{b_1}{b_2}=\dfrac24=\dfrac12$, $\dfrac{c_1}{c_2}=\dfrac{4}{12}=\dfrac13$. 2. Here $\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\ne\dfrac{c_1}{c_2}$, so the lines are parallel. 3. Therefore the pair has **no solution**. _Source: Karnataka SSLC (KSEEB) Class 10 Mathematics, Ch3 'Pair of Linear Equations in Two Variables', §3.2_

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Solving $x+y=14$ and $x-y=4$ gives

  1. $x=5,\ y=9$
  2. $x=10,\ y=4$
  3. $x=7,\ y=7$
  4. $x=9,\ y=5$
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Correct answer: D. $x=9,\ y=5$

1. Add the two equations: $2x=18$, so $x=9$. 2. Substitute: $9+y=14 \Rightarrow y=5$. 3. So $x=9,\ y=5$. _Source: Karnataka SSLC (KSEEB) Class 10 Mathematics, Ch3 'Pair of Linear Equations in Two Variables', §3.3 (elimination)_

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