College

We appreciate your visit to Which system is equivalent to tex left begin array l 5x 2 6y 2 50 7x 2 2y 2 10 end array right tex A. 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!

Which system is equivalent to

[tex]
\left\{
\begin{array}{l}
5x^2 + 6y^2 = 50 \\
7x^2 + 2y^2 = 10
\end{array}
\right.
[/tex]?

A.

[tex]
\left\{
\begin{aligned}
5x^2 + 6y^2 & = 50 \\
-21x^2 - 6y^2 & = 10
\end{aligned}
\right.
[/tex]

B.

[tex]
\left\{
\begin{aligned}
5x^2 + 6y^2 & = 50 \\
-21x^2 - 6y^2 & = 30
\end{aligned}
\right.
[/tex]

C.

[tex]
\left\{
\begin{aligned}
35x^2 + 42y^2 & = 250 \\
-35x^2 - 10y^2 & = -50
\end{aligned}
\right.
[/tex]

D.

[tex]
\left\{
\begin{array}{r}
35x^2 + 42y^2 = 350 \\
-35x^2 - 10y^2 = -50
\end{array}
\right.
[/tex]

Answer :

To find which system is equivalent to the given system:

[tex]\[
\left\{
\begin{array}{l}
5x^2 + 6y^2 = 50 \\
7x^2 + 2y^2 = 10
\end{array}
\right.
\][/tex]

we need to check each option to see which transformed system matches the original system of equations after possible manipulation.

Let's consider how these transformations could work:

### Original System:
1. [tex]\(5x^2 + 6y^2 = 50\)[/tex]
2. [tex]\(7x^2 + 2y^2 = 10\)[/tex]

We can multiply these equations to see how we might transform them:

### Transformations:
- Let's multiply the first equation by a number to make the coefficients match one of the options.

Multiply the first equation by 7:

1. [tex]\(7(5x^2 + 6y^2) = 7 \times 50\)[/tex]

This gives us:

[tex]\(35x^2 + 42y^2 = 350\)[/tex]

And multiply the entire second equation by [tex]\(-5\)[/tex]:

2. [tex]\(-5(7x^2 + 2y^2) = -5 \times 10\)[/tex]

This gives us:

[tex]\(-35x^2 - 10y^2 = -50\)[/tex]

### Check the Options:
Now we check which option matches this transformed system:

- Option 1:
[tex]\[
\left\{
\begin{aligned}
5x^2 + 6y^2 &= 50 \\
-21x^2 - 6y^2 &= 10
\end{aligned}
\right.
\][/tex]

- Option 2:
[tex]\[
\left\{
\begin{aligned}
5x^2 + 6y^2 &= 50 \\
-21x^2 - 6y^2 &= 30
\end{aligned}
\right.
\][/tex]

- Option 3:
[tex]\[
\left\{
\begin{aligned}
35x^2 + 42y^2 &= 250 \\
-35x^2 - 10y^2 &= -50
\end{aligned}
\right.
\][/tex]

- Option 4:
[tex]\[
\left\{
\begin{array}{r}
35x^2 + 42y^2 = 350 \\
-35x^2 - 10y^2 = -50
\end{array}
\right.
\][/tex]

From our transformed equations:

1. [tex]\(35x^2 + 42y^2 = 350\)[/tex]
2. [tex]\(-35x^2 - 10y^2 = -50\)[/tex]

We see that Option 4 matches our calculations:

[tex]\[
\left\{
\begin{array}{r}
35x^2 + 42y^2 = 350 \\
-35x^2 - 10y^2 = -50
\end{array}
\right.
\][/tex]

Thus, the correct equivalent system is:

Option 4

Thanks for taking the time to read Which system is equivalent to tex left begin array l 5x 2 6y 2 50 7x 2 2y 2 10 end array right tex A. 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