Answer :
Let's analyze the given system and the options to find which one is equivalent.
The original system is:
1. [tex]\(5x^2 + 6y^2 = 50\)[/tex]
2. [tex]\(7x^2 + 2y^2 = 10\)[/tex]
We are provided with four options, and we'll analyze each to see if they match the original system:
Option 1:
- [tex]\(5x^2 + 6y^2 = 50\)[/tex]
- [tex]\(-21x^2 - 6y^2 = 10\)[/tex]
Subtracting the first equation from the second:
[tex]\[
(-21x^2 - 6y^2) - (5x^2 + 6y^2) = 10 - 50
\][/tex]
[tex]\[
-26x^2 - 12y^2 = -40
\][/tex]
This equation doesn't simplify to match the original system.
Option 2:
- [tex]\(5x^2 + 6y^2 = 50\)[/tex]
- [tex]\(-21x^2 - 6y^2 = 30\)[/tex]
Subtracting the first equation from the second:
[tex]\[
(-21x^2 - 6y^2) - (5x^2 + 6y^2) = 30 - 50
\][/tex]
[tex]\[
-26x^2 - 12y^2 = -20
\][/tex]
This equation doesn't simplify to match the original system.
Option 3:
- [tex]\(35x^2 + 42y^2 = 250\)[/tex]
- [tex]\(-35x^2 - 10y^2 = -50\)[/tex]
Adding the two equations:
[tex]\[
(35x^2 + 42y^2) + (-35x^2 - 10y^2) = 250 - 50
\][/tex]
[tex]\[
32y^2 = 200
\][/tex]
This doesn't yield equations equivalent to the original system.
Option 4:
- [tex]\(35x^2 + 42y^2 = 350\)[/tex]
- [tex]\(-35x^2 - 10y^2 = -50\)[/tex]
Adding the two equations:
[tex]\[
(35x^2 + 42y^2) + (-35x^2 - 10y^2) = 350 - 50
\][/tex]
[tex]\[
32y^2 = 300
\][/tex]
Again, this doesn't match the original equations.
After checking all options, none directly match the original system:
[tex]\(5x^2 + 6y^2 = 50\)[/tex] and [tex]\(7x^2 + 2y^2 = 10\)[/tex].
This means that none of the provided options simplify directly to the original system of equations.
The original system is:
1. [tex]\(5x^2 + 6y^2 = 50\)[/tex]
2. [tex]\(7x^2 + 2y^2 = 10\)[/tex]
We are provided with four options, and we'll analyze each to see if they match the original system:
Option 1:
- [tex]\(5x^2 + 6y^2 = 50\)[/tex]
- [tex]\(-21x^2 - 6y^2 = 10\)[/tex]
Subtracting the first equation from the second:
[tex]\[
(-21x^2 - 6y^2) - (5x^2 + 6y^2) = 10 - 50
\][/tex]
[tex]\[
-26x^2 - 12y^2 = -40
\][/tex]
This equation doesn't simplify to match the original system.
Option 2:
- [tex]\(5x^2 + 6y^2 = 50\)[/tex]
- [tex]\(-21x^2 - 6y^2 = 30\)[/tex]
Subtracting the first equation from the second:
[tex]\[
(-21x^2 - 6y^2) - (5x^2 + 6y^2) = 30 - 50
\][/tex]
[tex]\[
-26x^2 - 12y^2 = -20
\][/tex]
This equation doesn't simplify to match the original system.
Option 3:
- [tex]\(35x^2 + 42y^2 = 250\)[/tex]
- [tex]\(-35x^2 - 10y^2 = -50\)[/tex]
Adding the two equations:
[tex]\[
(35x^2 + 42y^2) + (-35x^2 - 10y^2) = 250 - 50
\][/tex]
[tex]\[
32y^2 = 200
\][/tex]
This doesn't yield equations equivalent to the original system.
Option 4:
- [tex]\(35x^2 + 42y^2 = 350\)[/tex]
- [tex]\(-35x^2 - 10y^2 = -50\)[/tex]
Adding the two equations:
[tex]\[
(35x^2 + 42y^2) + (-35x^2 - 10y^2) = 350 - 50
\][/tex]
[tex]\[
32y^2 = 300
\][/tex]
Again, this doesn't match the original equations.
After checking all options, none directly match the original system:
[tex]\(5x^2 + 6y^2 = 50\)[/tex] and [tex]\(7x^2 + 2y^2 = 10\)[/tex].
This means that none of the provided options simplify directly to the original system of equations.
