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

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

1 Answer

4 votes

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)

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