To solve the system of equations, we can set the two expressions for `y` equal to each other:
2x² - x + 1 = x² + 4x + 7
Now, let's solve for `x`:
2x² - x + 1 - x² - 4x - 7 = 0
x² - 5x - 6 = 0
We can factor this quadratic equation:
(x - 6)(x + 1) = 0
So, the solutions for `x` are:
x = 6
x = -1
Now, let's find the corresponding `y` values for each `x` value:
For x = 6:
y = 2(6)² - 6 + 1
y = 2(36) - 6 + 1
y = 72 - 6 + 1
y = 67
For x = -1:
y = 2(-1)² - (-1) + 1
y = 2(1) + 1 + 1
y = 2 + 1 + 1
y = 4
So, the solutions of the system of equations are:
(x, y) = (6, 67)
(x, y) = (-1, 4)