Question

Which statements are true about the ordered pair (-3, 1) and the system of

equations?
(x - 4y = 6
| 3x + y = -8
Select each correct answer.
The ordered pair
is a solution to the first equation because it
makes the first equation true.
The ordered pair (-3, 1) is a solution to the second equation
because it makes the second equation true.
The ordered pair
is not a solution to the system because it
makes at least one of the equations false.
is a solution to the system because it
The ordered pair
makes both equations true.

Answer 1

The ordered pair (-3, 1) is not a solution to system because it makes at least one of the equations false

Solution:

Given system of equations are:

x - 4y = 6 ------- eqn 1

3x + y = -8 ------------ eqn 2

Given ordered pair is (-3, 1)

We have to check if the options are true

Let us substitute (x, y) = (-3, 1) in eqn 1

`-3 - 4(1) = 6\\\\-3 - 4 = 6\\\\-7\\eq 6`

Thus the given ordered pair (-3, 1) did not satisfy the first equation

Substitute (x, y) = (-3, 1) in eqn 2

`3(-3) + 1 = -8\\\\-9 + 1 = -8\\\\-8 = -8`

Thus the given ordered pair (-3, 1) satisfied the second equation

But for a ordered pair to be a solution to system of equations, it must satisfy both the equations

Thus the ordered pair (-3, 1) is not a solution to system because it makes at least one of the equations false