To solve this system of equations, we can set the two equations equal to each other since they both equal to y:
x^2 - 8 = x - 6
Next, we can rearrange the equation to set it equal to zero:
x^2 - x - 2 = 0
Now we can factor the quadratic equation:
(x - 2)(x + 1) = 0
Setting each factor equal to zero gives us two possible solutions for x:
x - 2 = 0 or x + 1 = 0
x = 2 or x = -1
Now that we have found the values of x, we can substitute them back into one of the original equations to find the corresponding values of y:
For x = 2:y = 2 - 6y = -4
For x = -1:y = (-1)^2 - 8y = 1 - 8y = -7
Therefore, the solutions to the system of equations are x = 2, y = -4 and x = -1, y = -7.
To solve this system of equations, we can set the two equations equal to each other since they both equal to y:
x^2 - 8 = x - 6
Next, we can rearrange the equation to set it equal to zero:
x^2 - x - 2 = 0
Now we can factor the quadratic equation:
(x - 2)(x + 1) = 0
Setting each factor equal to zero gives us two possible solutions for x:
x - 2 = 0 or x + 1 = 0
x = 2 or x = -1
Now that we have found the values of x, we can substitute them back into one of the original equations to find the corresponding values of y:
For x = 2:
y = 2 - 6
y = -4
For x = -1:
y = (-1)^2 - 8
y = 1 - 8
y = -7
Therefore, the solutions to the system of equations are x = 2, y = -4 and x = -1, y = -7.