Question

For a linear equation $2x+4y=8$, the other pair is for which the lines intersect.

• A. $3x+5y-8=0$
• B. $4x+8y-8=0$
• C. $6x+12y-8=0$

Answer 1

The correct option is A $3x+5y-8=0$

If a pair of linear equations are intersecting, then their slopes are not equal.

$\therefore$ $\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$

Given, $2x+4y-8=0$
$a_1=2,b_1=4$

Case 1:
$4x+8y-8=0$
$a_2=4,b_2=8$

$\frac{2}{4}=\frac{4}{8}$
Simplifying:
$\frac{1}{2}=\frac{1}{2}$
Thus, $4x+8y-8=0$ is not the other pair for the lines to be intersecting.

Case 2:
$6x+12y-8=0$
$a_2=6,b_2=12$

$\frac{2}{6}=\frac{4}{12}$
Simplifying:
$\frac{1}{3}=\frac{1}{3}$
Thus, $6x+12y-8=0$ is not the other pair for the lines to be intersecting. ​​​​

Case 3:
$3x+5y-8=0$
$a_2=3,b_2=5$

$\frac{2}{3}\ne \frac{4}{5}$

Thus, $3x+5y-8=0$ is other pair for the lines to be intersecting.