Question

- 2x + 5y = -15 How many solutions does the system have? V exactly one The solution to the system is 5x + 2y = -6 How could you solve this system using elimination? Check all that apply. * Multiply the first equation by 2 and the second equation by 5, then add. 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. Multiply the first equation by 5 and the second equation by 2, then subtract.

Answer 1

How many solutions does the system have?

✔ exactly one

The solution to the system is

(

⇒ 0,

⇒ -3).

Explanation:

the next two parts

Answer 2

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.

Explanation:

Given

`- 2x + 5y = -15`

`5x + 2y = -6`

Required

Steps to solve using elimination method

From the list of given options, option 2 and 3 are correct

This is shown below

Option 2

Multiply the first equation by 5

`5(- 2x + 5y = -15)`

`-10x + 25y = -75`

Multiply the second equation by 2.

`2(5x + 2y = -6)`

`10x + 4y = -12`

Add

`(-10x + 25y = -75) + (10x + 4y = -12)`

`-10x + 10x + 25y +4y = -75 - 12`

`29y = -87`

Notice that x has been eliminated

Option 3

Multiply the first equation by 2

`2(- 2x + 5y = -15)`

`-4x + 10y = -30`

Multiply the second equation by 5

`5(5x + 2y = -6)`

`25x + 10y = -30`

Subtract.

`(-4x + 10y = -30) - (25x + 10y = -30)`

`-4x + 25x + 10y - 10y= -30 +30`

`21x = 0`

Notice that y has been eliminated