Question

Given the system of linear equations. Choose all of the options that could be used to solve the system using addition

x + y =7
2x + y=

Multiply the first equation by -1 and add the equations together.

Multiply the second equation by -1 and the first equation by -1, then add the equations together.

Multiply the second equation by -1 and add the equations together.

Multiply the first equation by -2 and add the equations together.

Multiply the first equation by 2 and the second equation by -1, then add the equations together

Answer 1

The first, third, fourth, and fifth ones

Answer 2

• Multiply the first equation by -1 and add the equations together.
• Multiply the second equation by -1 and add the equations together.
• Multiply the first equation by -2 and add the equations together.
• Multiply the first equation by 2 and the second equation by -1, then add the equations together

Explanation:

In order to solve a system of equations using elimination method, the goal is always eliminate one of the variables using mathematical operations. So let's evaluate every option and we will see which of them is useful to eliminate one of the varibles:

Multiply the first equation by -1 and add the equations together.

`-x-y=-7\\\\2x+y-x-y=0-7\\\\x=-7`

This option is correct.

Multiply the second equation by -1 and the first equation by -1, then add the equations together.

`-x-y=-7\\-2x-y=0\\\\-x-y-2x-y=0-7\\\\-3x-2y=-7`

This option is incorrect.

Multiply the second equation by -1 and add the equations together.

`-2x-y=0\\\\-2x-y+x+y=7\\\\-x=7\\x=-7`

This option is correct

Multiply the first equation by -2 and add the equations together.

`-2x-2y=-14\\\\-2x-2y+2x+y=0-14\\\\-y=-14\\y=14`

This option is correct.

Multiply the first equation by 2 and the second equation by -1, then add the equations together.

`2x+2y=14\\-2x-y=0\\\\2x+2y-2x-y=0+14\\\\y=14`

This option is correct