Linear Equations – MCQs

By: Prof. Dr. Fazal Rehman Shamil | Last updated: January 31, 2025

Question 1:

\[
\text{What is the solution to the equation } 2x + 5 = 15 \text{?}
\]
\[
\text{(a) } x = 10, \quad \text{(b) } x = 5, \quad \text{(c) } x = -5, \quad \text{(d) } x = 2
\]
Answer: B

Question 2:

\[
\text{Solve for } x: \quad 3x – 7 = 2x + 5.
\]
\[
\text{(a) } x = 12, \quad \text{(b) } x = -12, \quad \text{(c) } x = 10, \quad \text{(d) } x = -10
\]
Answer: C

Question 3:

\[
\text{If } y = 3x + 4 \text{ and } x = 2, \text{ what is the value of } y?
\]
\[
\text{(a) } 10, \quad \text{(b) } 6, \quad \text{(c) } 12, \quad \text{(d) } 8
\]
Answer: A

Question 4:

\[
\text{Which of the following equations represents a straight line?}
\]
\[
\text{(a) } x^2 + y^2 = 4, \quad \text{(b) } y = 2x + 3, \quad \text{(c) } xy = 5, \quad \text{(d) } y^3 = x
\]
Answer: B

Question 5:

\[
\text{Find the value of } k \text{ if the equation } 4x + ky = 10 \text{ passes through } (1,2).
\]
\[
\text{(a) } 3, \quad \text{(b) } 4, \quad \text{(c) } 2, \quad \text{(d) } 1
\]
Answer: C

Question 6:

\[
\text{Solve for } x: \quad \frac{2x}{3} + \frac{4}{3} = 6.
\]
\[
\text{(a) } x = 6, \quad \text{(b) } x = 8, \quad \text{(c) } x = 12, \quad \text{(d) } x = 4
\]
Answer: A

Question 7:

\[
\text{If } 3x – 2y = 4 \text{ and } x + y = 5, \text{ find } x.
\]
\[
\text{(a) } 2, \quad \text{(b) } 3, \quad \text{(c) } 4, \quad \text{(d) } 1
\]
Answer: B

Question 8:

\[
\text{A line has a slope of } \frac{3}{4} \text{ and passes through (0,2). What is its equation?}
\]
\[
\text{(a) } y = \frac{3}{4}x + 2, \quad \text{(b) } y = \frac{4}{3}x + 2, \quad \text{(c) } y = \frac{3}{4}x – 2, \quad \text{(d) } y = \frac{4}{3}x – 2
\]
Answer: A

Question 9:

\[
\text{What is the solution to the system:} \quad x + y = 10, \quad x – y = 2?
\]
\[
\text{(a) } x = 6, y = 4, \quad \text{(b) } x = 5, y = 5, \quad \text{(c) } x = 4, y = 6, \quad \text{(d) } x = 7, y = 3
\]
Answer: A

Question 10:

\[
\text{The x-intercept of the line } 2x – 3y = 6 \text{ is:}
\]
\[
\text{(a) } (3,0), \quad \text{(b) } (-3,0), \quad \text{(c) } (6,0), \quad \text{(d) } (-6,0)
\]
Answer: A

Question 11:

\[
\text{The slope of the line passing through (2,3) and (4,7) is:}
\]
\[
\text{(a) } 2, \quad \text{(b) } \frac{4}{2}, \quad \text{(c) } \frac{7}{4}, \quad \text{(d) } \frac{3}{5}
\]
Answer: A

Question 12:

\[
\text{If } x = -1 \text{ is a solution of } 2x + 5 = ax – 1, \text{ find } a.
\]
\[
\text{(a) } 1, \quad \text{(b) } 2, \quad \text{(c) } 3, \quad \text{(d) } 4
\]
Answer: B

Question 13:

\[
\text{If } 4x – 7 = 5x + 3, \text{ then } x \text{ is:}
\]
\[
\text{(a) } 5, \quad \text{(b) } 10, \quad \text{(c) } -10, \quad \text{(d) } -5
\]
Answer: D

Question 14:

\[
\text{Which of the following equations has no solution?}
\]
\[
\text{(a) } 2x + 3 = 2x + 5, \quad \text{(b) } x + 2 = x + 2, \quad \text{(c) } 3x – 4 = 5x – 6, \quad \text{(d) } 4x + 2 = 4x + 2
\]
Answer: A

Question 15:

\[
\text{Find } k \text{ if the pair of equations } kx + 2y = 3 \text{ and } 6x + 4y = 5 \text{ has no solution.}
\]
\[
\text{(a) } 3, \quad \text{(b) } 4, \quad \text{(c) } 5, \quad \text{(d) } 6
\]
Answer: D

More MCQs on Algebra (Collected from Past Papers)

  1. Elementary Algebra – MCQs
  2. Algebraic Expressions – MCQs
  3. Algebraic Identities – MCQs
  4. Commutative Algebra – MCQs
  5. Linear Equations – MCQs
  6. Graphing Linear Equations – MCQs
  7. Inequalities in Algebra – MCQs
  8. Absolute Value Inequalities – MCQs
  9. Exponent – MCQs
  10. Exponential Functions – MCQs
  11. Logarithms – MCQs
  12. Polynomials – MCQs
  13. Factoring Methods – MCQs
  14. Polynomial Arithmetic – MCQs
  15. Quadratic Equation – MCQs
  16. Linear Algebra – MCQs
  17. Matrices in Algebra – MCQs
  18. Functions in Algebra – MCQs
  19. Sequences in Algebra – MCQs
  20. Arithmetic in Algebra – MCQs
  21. Combining Like Terms in Algebra – MCQs
  22. Abstract Algebra – MCQs
  23. Sets in Algebra – MCQs
  24. Algebra Calculator – MCQs

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