Answer:
x = -3, then y = -2
x = 2, then y = 3 both correct
Step by step explanation:
We can solve this system of equations algebraically by using substitution.
From the second equation, we can solve for y in terms of x:
y - x = 1
y = x + 1
Substituting y = x + 1 into the first equation, we get:
xy = 6
x(x + 1) = 6
Expanding the left side of the equation, we get:
x^2 + x = 6
Subtracting 6 from both sides, we get:
x^2 + x - 6 = 0
Factorizing the left side of the equation, we get:
(x + 3)(x - 2) = 0
Therefore, either x + 3 = 0 or x - 2 = 0. Solving for x, we get:
x = -3 or x = 2
Substituting these values of x into y = x + 1, we get:
if x = -3, then y = -2
if x = 2, then y = 3
So the solutions to the system of equations are (x, y) = (-3, -2) and (2, 3).