College

We appreciate your visit to Give all solutions of the nonlinear system of equations tex begin array l 7x 2 7y 2 84 35x 2 35y 2 336 end array. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Give all solutions of the nonlinear system of equations:

[tex]\[

\begin{array}{l}

7x^2 + 7y^2 = 84 \\

35x^2 + 35y^2 = 336

\end{array}

\][/tex]

Answer :

To solve the given system of nonlinear equations:

[tex]\[
\begin{align*}
1. & \quad 7x^2 + 7y^2 = 84 \\
2. & \quad 35x^2 + 35y^2 = 336 \\
\end{align*}
\][/tex]

First, notice that both equations can be simplified by dividing each term by their coefficients.

For the first equation:
[tex]\[
7x^2 + 7y^2 = 84
\][/tex]
Divide every term by 7:
[tex]\[
x^2 + y^2 = 12
\][/tex]

For the second equation:
[tex]\[
35x^2 + 35y^2 = 336
\][/tex]
Divide every term by 35:
[tex]\[
x^2 + y^2 = \frac{336}{35}
\][/tex]

Calculate the right side:
[tex]\[
x^2 + y^2 = \frac{336}{35} = 9.6
\][/tex]

Now we have a simpler system:
[tex]\[
\begin{align*}
1. & \quad x^2 + y^2 = 12 \\
2. & \quad x^2 + y^2 = 9.6 \\
\end{align*}
\][/tex]

Notice that the left-hand sides of both equations are the same, while the right-hand sides differ.

This situation indicates a contradiction: the same expression [tex]\(x^2 + y^2\)[/tex] cannot equal both 12 and 9.6 simultaneously. Therefore, there is no solution that satisfies both equations at the same time.

Thus, the system of equations does not have any real solutions.

Thanks for taking the time to read Give all solutions of the nonlinear system of equations tex begin array l 7x 2 7y 2 84 35x 2 35y 2 336 end array. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada