Question

Find the equation of the straight line passing through the point of intersection of the lines $2x+y-3=0$ and $5x+y-6=0$ and parallel to the line joining the points $(1,2)$ and $(2,1)$

• A. $x+y-2=0$
• B. $x+y+2=0$
• C. $x-y-2=0$
• D. None of these

Answer 1

The correct option is A $x+y-2=0$

Consider the given equation of the line.

$2x+y-3=0$ $...........\left(1\right)$

$5x+y-6=0$ $...........\left(2\right)$

$\left(2\right)-\left(1\right)$

$5x-2x+y-y-6+3=0$

$\Rightarrow 3x-3=0$

$\Rightarrow x=1$ sun in $\left(1\right)$

$2\left(1\right)+y-3=0$

$y-1=0$

$y=1$

$\Rightarrow$Point of intersection of above both lines is

$=(1,1)$

Given points

$A(1,2),B(2,1)$

Slope of $AB=\frac{1-2}{2-1}=\frac{-1}{1}=-1$

Since, the line is parallel to the the line $AB$, so the slope must be equal.

So, the equation of line passes through intersection point

$y-1=-1(x-1)$

$y-1=-x+1$

$x+y-2=0$

Hence, this is the answer.