Let's solve this nonlinear system of equations:

Given Equations:

1. $y = x^2 - 3$
2. $y = x^2 - 3x$

Step 1: Set the equations equal to each other

Since both equations equal $y$, we can set them equal to each other: $x^2 - 3 = x^2 - 3x$

Step 2: Simplify

Cancel $x^2$ from both sides: $-3 = -3x$

Divide both sides by $-3$: $x = 1$

Step 3: Solve for $y$

Substitute $x = 1$ into either equation. Using the first equation $y = x^2 - 3$: $y = 1^2 - 3 = -2$

Final Solution:

The solution is: $(1, -2)$

Thus, the correct choice is A, with the solution $(1, -2)$.

Would you like further clarification or a deeper explanation?

Related Questions:

1. What is the difference between linear and nonlinear systems of equations?
2. Can a nonlinear system have more than one solution?
3. How do substitution and elimination methods apply to solving systems of equations?
4. Why does canceling terms like $x^2$ work in this example?
5. How does graphing these equations confirm the solution?

Tip:

Always verify solutions by substituting them back into the original equations to ensure they satisfy both.