High School

Which system is equivalent to

\[
\begin{cases}
5x^2 + 6y^2 = 50 \\
7x^2 + 2y^2 = 10
\end{cases}
\]?

A.
\[
\begin{cases}
5x^2 + 6y^2 = 50 \\
-21x^2 - 6y^2 = 10
\end{cases}
\]

B.
\[
\begin{cases}
5x^2 + 6y^2 = 50 \\
-21x^2 - 6y^2 = 30
\end{cases}
\]

C.
\[
\begin{cases}
35x^2 + 42y^2 = 250 \\
-35x^2 - 10y^2 = -50
\end{cases}
\]

D.
\[
\begin{cases}
35x^2 + 42y^2 = 350 \\
-35x^2 - 10y^2 = -50
\end{cases}
\]

Answer :

Final answer:

The given system of equations can be solved using the method of elimination. The solution is x = ±√5 and y = ±√(25/6).

Explanation:

The given system of equations is:



5x^2 + 6y^2 = 50,

7x^2 - 6y^2 = 10.



We can solve this system by using the method of substitution or elimination.



Let's solve it using the method of elimination:



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