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Question
Find the point of intersection of the following pairs of lines:
2x − y + 3 = 0 and x + y − 5 = 0
Solution
The equations of the lines are as follows:
2x − y + 3 = 0 ... (1)
x + y − 5 = 0 ... (2)
Solving (1) and (2) using cross-multiplication method:
\[\frac{x}{5 - 3} = \frac{y}{3 + 10} = \frac{1}{2 + 1}\]
\[ \Rightarrow \frac{x}{2} = \frac{y}{13} = \frac{1}{3}\]
\[ \Rightarrow x = \frac{2}{3} \text { and y }= \frac{13}{3}\]
Hence, the point of intersection is \[\left( \frac{2}{3}, \frac{13}{3} \right)\].
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