Question:
<p>If a pair of linear equations has infinitely many solutions, then the lines representing them will be</p>
<p style="display:inline">parallel</p>
<p style="display:inline">always coincident</p>
<p style="display:inline">intersecting or coincident</p>
<p style="display:inline">always intersecting</p>
Step-by-Step Solution
Key Concept: A pair of linear equations has infinitely many solutions when the lines are coincident, which requires the ratios of the coefficients of x, y, and the constant terms to be equal.
<p>equation has infinite many solutions if<br />
<span class="math-tex">$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$</span><br />
i.e. always co-incident.</p>
Correct Answer: B