Find the equation of straight line which passes through the point (2,-3) and the point of intersection of the lines x+y +4 = 0 and 3x-y-8=0
2x-y-7 = 0
Any line through the intersection of the lines x + y + 4 = 0 and 3x - y - 8 = 0
Has the equation (x + y + 4) + λ (3x - y - 8) = 0-------------(1)
This equation also passes through the point (2,-3)
So, this point should satisfy the equation.
(2+3+4) + λ (6+3-8) = 0
3 + λ = 0
λ = -3
Putting the value of λ in equation 1 required equation is
(x + y + 4) -3(3x-y-8) = 0
x + y + 4 - 9x + 3y + 24 = 0
-8x + 4y + 28 = 0
-2x + y + 7 = 0
2x - y - 7 = 0
Alternative method
We can find the intersection between x+y+4 = 0 and 3x - y - 8 = 0
Adding both the equation 4x - 4 = 0
x = 1
Substituting x in equation (2)
1 + y + 4 = 0
y = -5
so, equation line which passes through (1,-5) and (2,-3)
y + 3 = −5+31−2(x−2)
2x - y - 7 = 0