Solve the simultaneous equations y^2=x^2-9 and y= x-1 .

We'll subtract y^2 both sides, in the 1st
equation:

x^2 -y^2 - 9 =
0

We'll add 9 both sides:

x^2
- y^2 = 9

We'll write the first equation as a difference of
squares:

x^2 - y^2 = 9

(x -
y)(x + y) = 9

We'll re-write the second
equation:

x - y = 1

We'll
substitute the second equation into the
first:

1*(x+y)=9

x + y =
9

We'll change the second equation and we'll write y with
respect to x.

y = x - 1

But x
+ y = 9

x + x - 1 = 9

We'll
combine like terms:

2x - 1 =
9

2x = 10

x =
5

y = 5 - 1

y =
4

The solution of the system is represented
by the pair: {5 ; 4}.