Question

Which statements are true about the ordered pair (−3, 1) and the system of equations? {x−4y=63x+y=−8 Select each correct answer. Responses The ordered pair (−3, 1) is a solution to the first equation because it makes the first equation true. The ordered pair , begin ordered pair negative 3 comma 1 end 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 , begin ordered pair negative 3 comma 1 end ordered pair, is a solution to the second equation because it makes the second equation true. The ordered pair (−3, 1) is not a solution to the system because it makes at least one of the equations false. The ordered pair , begin ordered pair negative 3 comma 1 end ordered pair, is not a solution to the system because it makes at least one of the equations false. The ordered pair (−3, 1) is a solution to the system because it makes both equations true.

Answer 1

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

Let's evaluate the ordered pair (-3, 1) in both equations:

For the first equation x - 4y = 6:

-3 - 4(1) = -3 - 4 = -7 (not equal to 6)

For the second equation 3x + y = -8:

3(-3) + 1 = -9 + 1 = -8 (equal to -8)

Therefore, the ordered pair (-3, 1) is not a solution to the first equation, but it is a solution to the second equation.

Since the ordered pair does not satisfy both equations simultaneously, it is not a solution to the system of equations. So, the correct statement is:

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