How do you find the intercept of two lines such as 3x-y-7=0 and x+5y+3=0?

Question

Please show steps

Answer 1

GIVEN the equations

3x - y- 7 = 0 and x + 5y + 3 = 0

I hope I understand your post correctly. My instinct tells me that you are looking for the coordinates of the point where these two lines intersect.

If my assumption is correct, then from the first equation

y = 3x - 7

and substituting this into the second equation,

x + 5(3x - 7) + 3 = 0

x + 15x -35 + 3 = 0

16x = 32

x = 2

Solving for "y",

y = 3(2) - 7

y = -1

The point of intersection of the two lines will be at the point

(2, - 1).

  

Answer 2

Solve the two as simultaneous equations,

3x - y - 7 = 0

y = 3x - 7 ---- (1)

x + 5y + 3 = 0

Subbing in equation (1),

x + 5(3x - 7 ) + 3 = 0

x + 15x - 35 + 3 = 0

16x - 32 = 0

x = 2

Sub x = 2 into (1)

y = 3(2) - 7

= -1

Hence the two lines intercept at (2, -1)