The linear equation 3x − 11y = 10 has

Question

The linear equation 3x − 11y = 10 has

1. A. Unique solution
2. B. Two solutions
3. C. Infinitely many solutions (Correct answer)
4. D. No solutions

Correct Answer

Option C — Infinitely many solutions

Detailed Solution & Explanation

The correct answer is Infinitely many solutions.

Key Points

• $3x - 11y = 10$ is a linear equation in two variables, of the general form $ax + by + c = 0$.
• Such an equation represents a straight line in the coordinate plane, and every point on that line is a solution.
• Since a line contains infinitely many points, the equation has infinitely many solutions.
• For any value of $x$ you choose, $y = \dfrac{3x - 10}{11}$ produces a matching value — the pairs never run out.

Additional Information

• Number of solutions by equation type:
  • One linear equation in one variable ($3x = 10$) → exactly one solution.
  • One linear equation in two variables → infinitely many solutions.
  • A pair of linear equations in two variables → one, none, or infinitely many, depending on the ratios of coefficients.
• For a pair $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$:
  • $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$ → unique solution (intersecting lines)
  • $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$ → no solution (parallel lines)
  • $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$ → infinitely many (coincident lines)