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UP Board Class 10 Linear Equations in One Variable — practice questions

Explore 32 free Linear Equations in One Variable questions in UP Board Class 10 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Linear Equations in One Variable questions and exercises with answers

Showing questions 1–30 of 32.

The present age of a father is twice the present age of his son. Five years ago, the father was three times as old as his son. What is the present age of the son?Read the answer and worked solution →Solve for f: 0.25(4f − 3) = 0.05(10f − 9)Read the answer and worked solution →A pair of linear equations in two variables that has no solution is called:Read the answer and worked solution →A pair of linear equations that has at least one solution is called:Read the answer and worked solution →If the two lines representing a pair of linear equations intersect at one point, the pair has:Read the answer and worked solution →If the two lines are parallel and never meet, the pair of equations has:Read the answer and worked solution →If the two lines are coincident (lie on top of each other), the pair has:Read the answer and worked solution →The graph of a linear equation in two variables is always a:Read the answer and worked solution →A dependent pair of linear equations is always:Read the answer and worked solution →For the pair a₁x+b₁y+c₁=0 and a₂x+b₂y+c₂=0, a unique solution exists when:Read the answer and worked solution →The condition $\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}$ corresponds to lines that are:Read the answer and worked solution →Which of the following is an algebraic method to solve a pair of linear equations?Read the answer and worked solution →The solution of a consistent pair of linear equations corresponds graphically to:Read the answer and worked solution →Solving x + y = 5 and x − y = 1 gives:Read the answer and worked solution →How many solutions does the system 2x + 3y = 5, 4x + 6y = 11 have?Read the answer and worked solution →For x − y = 1 and 2x − 2y = 2, how many solutions?Read the answer and worked solution →Which system has a unique solution?Read the answer and worked solution →A pair of equations is called inconsistent when:Read the answer and worked solution →Find the value of k so that kx + 3y = 7 and 4x + 6y = 14 represent coincident lines.Read the answer and worked solution →Solve by substitution: x + y = 10, x − y = 4.Read the answer and worked solution →Solve by elimination: 3x + 4y = 11 and 5x − 4y = 5.Read the answer and worked solution →Solve 2x + 3y = 12 and x − y = 1.Read the answer and worked solution →Find x and y in 5x − 7y = 2 and 7x − 5y = 22.Read the answer and worked solution →Solve 4x + 3y = 11 and 3x − 4y = 2.Read the answer and worked solution →A pair of equations gives a single solution iff:Read the answer and worked solution →The sum of two numbers is 25 and their difference is 5. Find them.Read the answer and worked solution →A father is 30 years older than his son. After 5 years the father will be three times as old as the son. Find their present ages.Read the answer and worked solution →Solve 1/x + 1/y = 1/3 and 1/x − 1/y = 1/12.Read the answer and worked solution →Five years ago A was thrice as old as B. Ten years later A will be twice as old as B. Find their present ages.Read the answer and worked solution →A two-digit number has digits whose sum is 9. Reversing the digits decreases the number by 27. Find the number.Read the answer and worked solution →

Worked practice questions

The present age of a father is twice the present age of his son. Five years ago, the father was three times as old as his son. What is the present age of the son?

  1. 5 years
  2. 8 years
  3. 10 years
  4. 15 years
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Correct answer: C. 10 years

Let the son's present age be x years. Then the father's present age is 2x years. Five years ago, son was (x − 5) and father was (2x − 5). **The condition gives:** 2x − 5 = 3(x − 5) = 3x − 15. Solving: 2x − 3x = −15 + 5 so −x = −10 and x = 10. The son is 10 years old now (and father is 20). **Verify:** five years ago son was 5, father was 15 = 3 × 5. ✓

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Solve for f: 0.25(4f − 3) = 0.05(10f − 9)

  1. f = 0.30
  2. f = 0.45
  3. f = 0.60
  4. f = 1.20
Show answer and solution

Correct answer: C. f = 0.60

Multiply both sides by 100 to clear decimals: 25(4f − 3) = 5(10f − 9). **Expand:** 100f − 75 = 50f − 45. Transpose: 100f − 50f = 75 − 45 so 50f = 30 and f = 0.60. A quick decimal check: LHS = 0.25 × (2.4 − 3) = 0.25 × (−0.6) = −0.15. RHS = 0.05 × (6 − 9) = 0.05 × (−3) = −0.15. ✓

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A pair of linear equations in two variables that has no solution is called:

  1. inconsistent
  2. consistent
  3. unique
  4. dependent
Show answer and solution

Correct answer: A. inconsistent

A pair with no solution is inconsistent.

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More Mathematics topics

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