Nonlinear Systems

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Solve each system of nonlinear equations.

\(\textbf{1)}\) \(x^2+y^2=8\)
\(\) \(y=x\)


\(\textbf{2)}\) \(x^2+y^2=25\)
\(\) \(y=\frac{3}{4}x\)


\(\textbf{3)}\) \(y=x^2+2\)
\(\) \(y=2\)


\(\textbf{4)}\) \(y=x^2-2\)
\(\) \(y=2\)


\(\textbf{5)}\) \(y=x^2-3\)
\(\) \(y=-x^2+5\)


\(\textbf{6)}\) \(y=x^2+2\)
\(\) \(y=2x+2\)


\(\textbf{7)}\) \(y=x^2+2\)
\(\) \(y=2x+1\)


\(\textbf{8)}\) \(y=x^2+2\)
\(\) \(y=2x\)


\(\textbf{9)}\) \(y=x^2+2\)
\(\) \(y=x^2+4\)


Graph each system of inequalities.

\(\textbf{10)}\) \( y\gt x^2 \)
\(\) \( y\lt4 \)


\(\textbf{11)}\) \( x^2+y^2\le36 \)
\(\) \( y\ge3 \)


\(\textbf{12)}\) \( y\ge x^2-4 \)
\(\) \( y\le -x^2+6 \)


\(\textbf{13)}\) \( y\le x^2+3 \)
\(\) \( y\ge x^2-5 \)


Related Pages\(\)

\(\bullet\text{ Solving Systems with Substitution}\)
\(\,\,\,\,\,\,\,\,y=−2x+5\)
\(\,\,\,\,\,\,\,\,y=x-1…\)
\(\bullet\text{ Solving Systems with Elimination}\)
\(\,\,\,\,\,\,\,\,7x+4y=31 \)
\(\,\,\,\,\,\,\,\,3x+2y=15…\)
\(\bullet\text{ Graphing Systems of Inequalities}\)
\(\,\,\,\,\,\,\,\,y\lt-3x+2 \)
\(\,\,\,\,\,\,\,\,y\ge\frac{1}{2}x-1…\)
\(\bullet\text{ 3 variable systems}\)
\(\,\,\,\,\,\,\,\,2x+3y−5z=−7 \)
\(\,\,\,\,\,\,\,\,3x−6y+4z=3 \)
\(\,\,\,\,\,\,\,\,x+4y+2z=15…\)
\(\bullet\text{ Andymath Homepage}\)

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In Summary

Solving non-linear systems involves finding the values of the variables that simultaneously satisfy a system of equations with non-linear expressions. This can be done using various methods, such as substitution, elimination, and graphing.

Solving non-linear systems is typically covered in a high school or college algebra class.

A common mistake when solving non-linear systems is to forget to check whether the solution obtained is a valid solution to the original system of equations. It is important to carefully substitute the values of the variables back into the equations in the system to ensure that they are satisfied.

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