Question

Find the equation of the line which passes through the point of intersection of the lines $x+2y-3=0$ and $4x-y+7=0$ and is parallel to the line $y-x+10=0$?

• A. $2x+2y+5=0$
• B. $3y-3x=10$
• C. $3x+2y-8=0$
• D. None of these

Answer 1

Answer: (B)

$3y-3x=10$

Let equation of any straight line passing through the point of intersection of two given straight line be

$k(x+2y-3)+(4x-y+7)=0$

=>$(k+4)x+(2k-1)y+(7-3k)=0$............(1)

If the straight be parallel to the straight line $y-x+10=0$ be

then,

$\frac{k+4}{-1}=\frac{2k-1}{1}$

$k+4=1-2k$

$k+2k=1-4$

$3k=-3$

$k=-1$

Now substitute the value of k in equation (1)

$(-1+4)x+(2\times -1-1)y+(7-3\times -1)=0$

$3x+-3y+10=0$

$3y-3x=10$

This is the required equation of the straight line.