Question

The line passing through the point of intersection of line $x+y-2=0$ and $2x-y+1=0$ and origin is

• A. $5x-y=0$
• B. $5x+y=0$
• C. $x+5y=0$
• D. $x-5y=0$

Answer 1

Answer: (A)

$5x-y=0$

Consider the lines $x+y-2=0$ and $2x-y+1=0$

To find the point of intersection, solve both the equations to find $x$ and $y$

Adding both equations we get,

$3x-1=0$ $⟹x=\frac{1}{3}$

Substituting for $x$ in $x+y-2=0$, we get,

$\frac{1}{3}+y-2=0$

$y=2-\frac{1}{3}=\frac{6-1}{3}=\frac{5}{3}$

Substituting for $x$ and $y$ in each of the four options given, we can see that Option A is right

i.e., $5x-y=0$