Question

The equation of the line joining through the points of intersection of lines 2x - y + 3 = 0 and 3x + y + 7 = 0 and perpendicular to 2x - 3y + 4 = 0 , is

Answer 1

Step-by-step explanation:

What is the equation of a line passing through the point of intersection of lines 2x−y+3=0 and 3x+2y−7=0 and perpendicular to 2x−3y+4=0 ?

000000000000000000000000000000000000000000000

line perpendicular to 2x−3y+4=0 is given by 3x+2y+c=0

If one is alert one could see one of the given lines meets the criterion.

So 3x+2y−7=0 is the required line.

However if one fails to see it, one can use linear combination of 2x−y+3=0 and 3x+2y−7=0

A(2x−y+3)+B(3x+2y−7)=3x+2y+c

x(2A+3B)+y(2B−A)+3a−7B=3x+2y+c

Compare coefficients,

2A+3B=3 and 2B−A=2.

solving we get A=0 and B=1⟹

3x+2y−7=3x+2y+c

So 3x+2y−7=0 is the required line