Find the solutions to the system of nonlinear equations given by:
\[
\left\{\begin{array}{l}
y=-3 x+3 \\
y=-x^{2}+3
\end{array}\right.
\]

Answer

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Answer

The solutions to the system of nonlinear equations are \(\boxed{(0, 3)}\) and \(\boxed{(3, -6)}\)

Steps

Step 1 ：Set the two equations equal to each other: \(-3x + 3 = -x^2 + 3\)

Step 2 ：Solve the equation for x to get: \(x = 0\) and \(x = 3\)

Step 3 ：Substitute the x-values into one of the original equations to find the corresponding y-values: \(y = -3(0) + 3 = 3\) and \(y = -3(3) + 3 = -6\)

Step 4 ：The solutions to the system of nonlinear equations are \(\boxed{(0, 3)}\) and \(\boxed{(3, -6)}\)

Find the solutions to the system of nonlinear equations given by:\[\left\{\begin{array}{l}y=-3 x+3 \\y=-x^{2}+3\end{array}\right.\]

Answer

Popular Problems

Find the solutions to the system of nonlinear equations given by:
\[
\left\{\begin{array}{l}
y=-3 x+3 \\
y=-x^{2}+3
\end{array}\right.
\]