Final answer:
To solve the system of equations, we use the method of substitution. The solution set is {(3, 6), (-2, 1)}.
Step-by-step explanation:
To solve the given system of equations, we will use the method of substitution. We have two equations:
x² - y = 3
x - y = -3
We rearrange the second equation to solve for x: x = -3 + y.
Substitute this value of x in the first equation:
(-3 + y)² - y = 3
Simplify and solve for y:
9 - 6y + y² - y = 3
Rearrange to form a quadratic equation:
y² - 7y + 6 = 0
Factorize: (y - 1)(y - 6) = 0
So, y = 1 or y = 6.
Substitute each value of y back into the equation x = -3 + y to find the corresponding values of x:
If y = 1, then x = -3 + 1 = -2.
If y = 6, then x = -3 + 6 = 3.
Therefore, the solution set is {(x, y) : (3, 6), (-2, 1)}.