To find the solution to the given nonlinear system:
[tex]\[
\begin{aligned}
x + y & = 9 \\
x^2 + y^2 & = 53
\end{aligned}
\][/tex]
We are given that one of the values for [tex]\( x \)[/tex] is [tex]\( 2 \)[/tex]. We need to find the corresponding value for [tex]\( y \)[/tex].
First, substitute [tex]\( x = 2 \)[/tex] into the first equation:
[tex]\[
2 + y = 9
\][/tex]
Now, solve for [tex]\( y \)[/tex]:
[tex]\[
y = 9 - 2 = 7
\][/tex]
Next, we need to verify that the second equation is satisfied with [tex]\( x = 2 \)[/tex] and [tex]\( y = 7 \)[/tex]:
[tex]\[
x^2 + y^2 = 2^2 + 7^2 = 4 + 49 = 53
\][/tex]
Since both the first and second equations are satisfied, we have found a valid solution.
Therefore, one of the solutions for the system is [tex]\( (2, 7) \)[/tex].
So, the completed sentence is:
The following nonlinear system has two solutions, one of which is [tex]\((2, 7)\)[/tex].
