Solve the system of equations.
y = 2x² – 3
y = 3x – 1
To solve this system of equations, we need to set the two equations equal to each other and then solve for x.
2x² - 3 = 3x - 1
Rearrange the equation to set it equal to zero:
2x² - 3x + 2 = 0
We can solve this quadratic equation by factoring or using the quadratic formula. Factoring may not work here, so let's use the quadratic formula:
x = (-(-3) ± √((-3)² - 4(2)(2)))/(2(2))
x = (3 ± √(9 - 16))/4
x = (3 ± √(-7))/4
Since the square root of a negative number is not a real number, there are no real solutions to this system of equations.