Question

Given equations are $x+3y=42$ and $3x-y=8$
In the system of equations above, how many points of intersection do the equations share and find their relationship, if any.

• A. Zero, and the lines are parallel.
• B. Infinitely many, and the lines are the same line.
• C. One, and the lines have no relationship.
• D. One, and the lines are perpendicular.

Answer 1

The correct option is D One, and the lines are perpendicular.

As per given equation $x+3y=42$

$\Rightarrow 3y=-x+42$

$\Rightarrow y=-\frac{1}{3}x+42$

The slope of line is $-\frac{1}{3}$

And given the equation $3x-y=8$

$\Rightarrow -y=-3x+8$

$\Rightarrow y=3x-8$

The slope of line is equation $3$.

The first line slope is $-\frac{1}{3}$ and second line slope is $3$.These slopes are negative reciprocals, so the lines through the points are perpendicular to each other.

So (D) is the correct answer.