MP Board · Class 10 · Mathematics · Pair of Linear Equations in Two VariablesFor what value of $k$ does the pair of linear equations $x + 2y - 3 = 0$ and $5x + ky + 7 = 0$ represent parallel lines?
For parallel lines (no solution), the algebraic condition is:\n$$\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$$\n\nComparing given equations with standard form:\n- $a_1 = 1, b_1 = 2, c_1 = -3$\n- $a_2 = 5, b_2 = k, c_2 = 7$\n\nNow, set:\n$$\frac{1}{5} = \frac{2}{k}$$\n\nCross-multiplying gives:\n$$k = 10$$\n\nAlso, $\frac{2}{10} \neq \frac{-3}{7}$, which holds true. Thus, $k = 10$.
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Pair of Linear Equations in Two Variables.
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Pair of Linear Equations in Two Variables.
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Pair of Linear Equations in Two Variables.