Answer:
Multiply the first equation by 5 and the second equation by 2. Then add.
Multiply the first equation by 2 and the second equation by 5, then subtract.
Step-by-step explanation:
Given
![- 2x + 5y = -15](https://tex.z-dn.net/?f=-%202x%20%2B%205y%20%3D%20-15)
![5x + 2y = -6](https://tex.z-dn.net/?f=5x%20%2B%202y%20%3D%20-6)
Required
Steps to solve using elimination method
<em>From the list of given options, option 2 and 3 are correct</em>
<em>This is shown below</em>
Option 2
Multiply the first equation by 5
![5(- 2x + 5y = -15)](https://tex.z-dn.net/?f=5%28-%202x%20%2B%205y%20%3D%20-15%29)
![-10x + 25y = -75](https://tex.z-dn.net/?f=-10x%20%2B%2025y%20%3D%20-75)
Multiply the second equation by 2.
![2(5x + 2y = -6)](https://tex.z-dn.net/?f=2%285x%20%2B%202y%20%3D%20-6%29)
![10x + 4y = -12](https://tex.z-dn.net/?f=10x%20%2B%204y%20%3D%20-12)
Add
![(-10x + 25y = -75) + (10x + 4y = -12)](https://tex.z-dn.net/?f=%28-10x%20%2B%2025y%20%3D%20-75%29%20%2B%20%2810x%20%2B%204y%20%3D%20-12%29)
![-10x + 10x + 25y +4y = -75 - 12](https://tex.z-dn.net/?f=-10x%20%2B%2010x%20%2B%2025y%20%2B4y%20%3D%20-75%20-%2012)
![29y = -87](https://tex.z-dn.net/?f=29y%20%3D%20-87)
Notice that x has been eliminated
Option 3
Multiply the first equation by 2
![2(- 2x + 5y = -15)](https://tex.z-dn.net/?f=2%28-%202x%20%2B%205y%20%3D%20-15%29)
![-4x + 10y = -30](https://tex.z-dn.net/?f=-4x%20%2B%2010y%20%3D%20-30)
Multiply the second equation by 5
![5(5x + 2y = -6)](https://tex.z-dn.net/?f=5%285x%20%2B%202y%20%3D%20-6%29)
![25x + 10y = -30](https://tex.z-dn.net/?f=25x%20%2B%2010y%20%3D%20-30)
Subtract.
![(-4x + 10y = -30) - (25x + 10y = -30)](https://tex.z-dn.net/?f=%28-4x%20%2B%2010y%20%3D%20-30%29%20-%20%2825x%20%2B%2010y%20%3D%20-30%29)
![-4x + 25x + 10y - 10y= -30 +30](https://tex.z-dn.net/?f=-4x%20%20%2B%2025x%20%2B%2010y%20-%2010y%3D%20-30%20%2B30)
![21x = 0](https://tex.z-dn.net/?f=21x%20%3D%200)
<em>Notice that y has been eliminated</em>