Question

Do the following two straight lines intercect? If yes, then where?
i. $2x+3y=5$
ii. $3x+2y=0$

• A. Yes, they intersect at $(-2,3)$
• B. Yes, they intersect at $(4,-3)$
• C. Yes, they intersect at $(2,1)$
• D. No, they do not intersect.

Answer 1

The correct option is A Yes, they intersect at $(-2,3)$

Given straight lines, $2x+3y=5$ and $3x+2y=0$
Since the slopes of the given two straight lines are different they intersect.

From the second line we get, $y=-\frac{3x}{2}$

Putting this in the equation of first line,
$2x+3(-\frac{3x}{2})=5$
$4x-9x=10$
$\Rightarrow x=-2$

$y=-\frac{3x}{2}=3$

The point of intersection of the two lines is $(-2,3)$