Question

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

Example:
x+y+7
x-y=3
are those parallel or perpendicular or none

Answer 1

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

Answer 2

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