which system is equivalent to $\begin{cases}5x^{2}+6y^{2}=50\\7x^{2}+2y^{2}=10end{cases}$?\n$\begin{cases}5x^…

which system is equivalent to $\begin{cases}5x^{2}+6y^{2}=50\\7x^{2}+2y^{2}=10end{cases}$?\n$\begin{cases}5x^{2}+6y^{2}=50\\-21x^{2}-6y^{2}=10end{cases}$\n$\begin{cases}5x^{2}+6y^{2}=50\\-21x^{2}-6y^{2}=30end{cases}$\n$\begin{cases}35x^{2}+42y^{2}=250\\-35x^{2}-10y^{2}=-50end{cases}$\n$\begin{cases}35x^{2}+42y^{2}=350\\-35x^{2}-10y^{2}=-50end{cases}$

which system is equivalent to $\begin{cases}5x^{2}+6y^{2}=50\\7x^{2}+2y^{2}=10end{cases}$?\n$\begin{cases}5x^{2}+6y^{2}=50\\-21x^{2}-6y^{2}=10end{cases}$\n$\begin{cases}5x^{2}+6y^{2}=50\\-21x^{2}-6y^{2}=30end{cases}$\n$\begin{cases}35x^{2}+42y^{2}=250\\-35x^{2}-10y^{2}=-50end{cases}$\n$\begin{cases}35x^{2}+42y^{2}=350\\-35x^{2}-10y^{2}=-50end{cases}$

Answer

Explanation:

Step1: Multiply equations to get equivalent system

Multiply the first equation $5x^{2}+6y^{2}=50$ by $7$: $7(5x^{2}+6y^{2})=7\times50$, which simplifies to $35x^{2}+42y^{2}=350$. Multiply the second - equation $7x^{2}+2y^{2}=10$ by $- 5$: $-5(7x^{2}+2y^{2})=-5\times10$, which simplifies to $-35x^{2}-10y^{2}=-50$.

Answer:

$\begin{cases}35x^{2}+42y^{2}=350\-35x^{2}-10y^{2}=-50\end{cases}$