Question

Line $1$: $4x+2y=6$ and Line $2$: $y=px+q$ have infinite number of solutions, then $p$ and $q$ are

• A. $-2,3$
• B. $2,3$
• C. $-2,-3$
• D. $-4,3$

Answer 1

The correct option is A $-2,3$

Given:
Line $1$: $4x+2y=6$
Line $2$: $y=px+q$
Step 1: Write Line $1$: $4x+2y=6$ as $y=mx+b$ form.
So,
$4x+2y=6$
$2y=-4x+6$
$\Rightarrow y=-2x+3$
Step 2: $y=-2x+3$ and $y=px+q$ have infinite number of solutions. Hence, their slopes and intercepts will be same.
So,
$p=-2$ and $q=3$