Multiple choice

Which of the following pairs of equations represents parallel lines?

  1. x + y = 13, x – y = 1

  2. 2x + 3y = 5, 4x + 6y = 12

  3. x + 3y = 7, 3x + y = 2

  4. x + y = 4, x – y = 0
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The two lines a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 will be parallel if $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$. $\because$        $\frac{a_1}{a_2} = \frac{2}{4} = \frac{1}{2}$, $\frac{b_1}{b_2} = \frac{3}{6} = \frac{1}{2}$ and $\frac{c_1}{c_2} = \frac{5}{12} $. $\therefore$        $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$ Hence, 2x + 3y = 5 and 4x + 6y = 12 are parallel lines.

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