Question

Which of the following is the correct classification of the system of equations below?

-x+2y=10
6y=-12x+1
Parallel
Coincident
Intersecting

Answer 1

Correct answer is C.

$-x+2y=10 \\2y=x+10 \\y= \frac{1}{2} x+5 \\m_1= \frac{1}{2} \\ \\6y=-12x+1 \\y=-2x+ \frac{1}{6} \\m_2=-2 \\ \\m_1 \times m_2=\frac{1}{2} (-2)=-1 \Rightarrow \text{Lines are perpendicular}$

Therefore, lines are intersecting.