Question

Find the point of intersection of the following pairs of lines:

2x − y + 3 = 0 and x + y − 5 = 0

Answer 1

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 \[\left( \frac{2}{3}, \frac{13}{3} \right)\].