Mathematics · Quantitative Aptitude

Linear Equations

196 Questions

Linear equations involve solving for unknown variables in single or multi variable systems. These questions test algebraic manipulation and logical consistency skills. They are a core component of quantitative aptitude and advanced mathematics tests.

Solving simultaneous equationsSingle variable equationsSystem consistency checksIndeterminate equationsMatrix form solutions

Linear Equations Questions

Multiple choice

Solve: x + 2y = 3 and 2x + y = 3

  1. x = 1, y = 0

  2. x = 1, y = 1

  3. x = 2, y = 1/2

  4. No solution exists for this set.

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Substitute x = 3 - 2y in the second equation.  

6 - 4y + y = 3 Or y = 1 And x = 1

Multiple choice

Solve: 5x - 9y = 2 and 10x - 18y = 4

  1. (0, 0)

  2. (1, 0)

  3. (3, 2)

  4. Infinite solutions

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

As both the lines are same, all the points lying on the line will be the solution. As the lines are same, so there are infinite solutions.

Multiple choice

Solve: x + y = 2 and ax + by = a + b

  1. (a, 1)

  2. (a, b)

  3. (1, 1)

  4. (1, b)

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Multiply the first equation by 'a' and subtract from second. (b - a)y = b - a Or y = 1 and x = 1

Multiple choice

Let k be the solution of the equation 2k + 4 = 8 and l be the solution of the equation 3I + 9 = 3 (9 - 4). Which of the following options is/are not correct?

  1. k + I = 4

  2. k / l = 1

  3. k - l = 0

  4. k x l = 2

  5. All of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

2k + 4 = 8 => 2k = 4 => k = 2 --------- (1) 3I + 9 = 3 (9 - 4) => 3I + 9 = 3 x 5 => 3I = 15 - 9 => 3I = 6 => I = 2 ------------- (2)

Therefore, k x l = 4 Hence, the option is incorrect. Therefore, it is the correct answer.