Question

Which of these pairs of lines are parallel?

• A. y = 3; 2x - 7y - 5 = 0
• B. 3y - 2x = 2; 3x - 2y = 2
• C. $\sqrt{3}x-y=2;\sqrt{6}x-\sqrt{2}y=2$
• D. $\frac{x}{3}+\frac{y}{2}=1;x+\frac{3y}{2}=3$

Answer 1

The correct option is C $\sqrt{3}x-y=2;\sqrt{6}x-\sqrt{2}y=2$

Write the two equations in the general form where
$a_{1}x+b_{1}y+c_1=0and$
$a_{2}x+b_{2}y+c_2=0$,
For two lines to be parallel, $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}For\sqrt{3x}-y=2;\sqrt{6x}-\sqrt{2}y=2,\frac{a_1}{a_2}=\frac{\sqrt{3}}{\sqrt{6}}=\frac{1}{\sqrt{2}}\frac{b_1}{b_2}=\frac{-1}{-\sqrt{2}}=\frac{1}{\sqrt{2}}\frac{c_1}{c_2}=\frac{-2}{-2}=1Hence\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}.$