Find the coordinates of the point of intersecton of the lines 2x – y + 3 = 0 and x + y – 5 = 0.

Solution :

Solving simultaneously the equations 2x – y + 3 = 0 and x + y – 5 = 0, we obtain

$$x\over {5 – 3}$$ = $$y\over {3 + 10}$$ = $$1\over {2 + 1}$$

$$\implies$$ $$x\over 2$$ = $$y\over 13$$ = $$1\over 3$$

$$\implies$$ x = $$2\over 3$$ , y = $$13\over 3$$

Hence, (2/3, 13/3) is the required point of intersection.

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