Question

Find an equation of a line passing through the point of intersection of x + 2y – 4 = 0 and 3x + y + 3 = 0, and

make the intercept on both the axes equal in magnitude and opposite in signs.​

Answer 1

Answer:

x-y-5=0

Step-by-step explanation:

x+2y-4=0.....(1)

3x+y+3=0.....(2)

solve 1 and 2nd that is rhe intersection point of both line, it will be (-2,3)

let the equation of required line is given

$\frac{x}{a} + \frac{y}{b} = 1 \\ ...(3)$

where a and b are the intercept on x and y axis respectively.

$a = - b(given)$

line is passing throught (-2,3) so put in equation 3

$\frac{ - 2}{a} + \frac{3}{ - a} = 1 \\ \frac{ - 2}{a} - \frac{3}{a} = 1 \\ a = 5 \\ and \: solve \: b \\ b = 5$

so equation of line is

x/-5+y/5=1

-x/5+y/5=1

-x+y=5

$x - y - 5 = 0$