Final answer:
The nonlinear system of equations y=x² -3 and y=x² -3x is solved by equating them and then solving for x, which is found to be 1. Substituting x back into one of the equations gives y=-2, so the solution to the system is x=1 and y=-2.
Step-by-step explanation:
To solve the nonlinear system of equations y=x² -3 and y=x² -3x, we need to set them equal to each other since they both equal y:
x² - 3 = x² - 3x
By subtracting x² from both sides, we get:
-3 = -3x
Now, we divide both sides by -3 to solve for x:
x = 1
Substitute x back into either of the original equations to find y:
y = (1)² - 3 = 1 - 3 = -2
Therefore, the solution to the system of equations is x=1 and y=-2.