Question

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

Answer 1

Given:

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

Adding (1) and (2)

`\begin{gathered} (1)/(2)x+10y-(1)/(2)x+5y=10+5 \\ 15y=15 \\ y=1 \end{gathered}`

Substitute y=1 in equation(1)

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

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