Find the points of intersection of the following pairs of lines:
$2 x - y + 3 = 0$ and $x + y - 5 = 0$

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Solution

$2 x - y + 3 = 0 . . . . . (1)$
$x + y - 5 = 0 . . . . . (2)$
Adding equation $(1) & (2)$ , we have
$(2 x - y + 3) + (x + y - 5) = 0$
$3 x - 2 = 0$
$\Rightarrow x = \frac{2}{3}$
Substituting the value of $x$ in equation $(2)$ , we have
$\frac{2}{3} + y - 5 = 0$
$\Rightarrow y = 5 - \frac{2}{3} = \frac{13}{3}$
Hence the point of intersection of the given lines is $(\frac{2}{3}, \frac{13}{3})$ .

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Find the points of intersection of the following pairs of lines:2x−y+3=0 and x+y−5=0

2x−y+3=0.....(1)x+y−5=0.....(2)Adding equation (1)&(2), we have(2x−y+3)+(x+y−5)=03x−2=0⇒x=23Substituting the value of x in equation (2), we have23+y−5=0⇒y=5−23=133Hence the point of intersection of the given lines is (23,133).

Find the points of intersection of the following pairs of lines:
$2 x - y + 3 = 0$ and $x + y - 5 = 0$