Question

determine if the lines 1/2x + 10y = 10 and -1/2x + 5y =5 are parallel.

Answer 1

Given:

$\begin{gathered} \frac{1}{2}x+10y=10\ldots\text{ (1)} \\ -\frac{1}{2}x+5y=5\ldots\text{ (2)} \end{gathered}$

Adding (1) and (2)

$\begin{gathered} \frac{1}{2}x+10y-\frac{1}{2}x+5y=10+5 \\ 15y=15 \\ y=1 \end{gathered}$

Substitute y=1 in equation(1)

$\begin{gathered} \frac{1}{2}x+10y=10 \\ \frac{1}{2}x+10(1)=10 \\ \frac{1}{2}x=10-10 \\ \frac{1}{2}x=0 \\ x=0 \end{gathered}$

The lines are not parallel because they intersect at (0,1)