Question

Which statements about this system of equations are true? Check all that apply 2 x minus 7 y = negative 13. Negative 2 x + 11 y = 1. The x-variable will be eliminated when adding the system of equations. The y-variable will be eliminated when adding the system of equations. The sum of the system of equations is 4 y = negative 12. x = 17 y = negative 3 There are infinitely many solutions to the system of equations.

Answer 1

A, C, E

This you answer!

Answer 2

1 and 3.

Explanation:

The given system of equations

`2x-7y=-13` ...(1)

`-2x+11y=1` ... (2)

Here, coefficients of x have same values with opposite signs.

The x-variable will be eliminated when adding the system of equations.

Add (1) and (2), we get

`2x-7y-2x+11y=-13+1`

`4y=-12`

Divide both sides by 4.

`y=-3`

Put y=-3 in (1).

`2x-7(-3)=-13`

`2x+21=-13`

`2x=-13-21`

`2x=-34`

Divide both sides by 2.

`x=-17`

So, the given system of equations have unique solution, i.e., (-17,-3).

Therefore, the correct options are 1 and 3.