Solve the system of equations by the method of substitution.x^2 x - y = 1

We'll re-write the first
equation:

x^2 - y^2 = 9 (1)

x - y = 1
(2)

To solve using the substitution method, we'll write x with
respect to y, from the 2nd equation:

x = 1 + y
(3)

We'll substitute (3) in
(1):

(1+y)^2 - y^2 = 9 (4)

We notice
that the equation (4) is a difference of squares:

(1+y)^2 - y^2 = (1
+ y - y)(1 + y + y)

We'll eliminate and combine like terms inside
the brackets:

(1+y)^2 - y^2 = 1 +
2y

We'll re-write (4):

1 + 2y =
9

2y = 9 - 1

2y =
8

y =
4

We'll substitute y in
(3):

x = 1 + 4

x =
5

The solution of the system is {5 ;
4}.