Question

How can you tell if two equations for parallel lines or perpendicular lines. please explain?

Answer 1

To find out if they are parallel we need to see if the gradient is the same, to do this we need to get y in terms of x:
assuming the first equation is x+y+7=0
y=-x-7
and
y=x-3
The gradient is the coefficient of x (the number infront of x)
For equation 1 the gradient is -1, and for number 2 it is 1, therefore they are not parallel.
However to check if they are perpendicular we need to see if their gradients multiply to equal -1.
-1*1=-1 therefore they are perpendicular

Answer 2

X + y = 7
x -  y = 3
   2x = 10
    2      2
     x = 5
5 + y = 7
-5       -5
     y = 2
(x, y) = (5, 2)