Which statements are true about the ordered pair (5, −6) and the system of equations? {x+y=−1 3x−y=21 Select each correct answer

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3 years ago

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Which statements are true about the ordered pair (5, −6) and the system of equations? {x+y=−1 3x−y=21 Select each correct answer

. The ordered pair (5, −6) is a solution to the first equation because it makes the first equation true. The ordered pair (5, −6) is a solution to the second equation because it makes the second equation true. The ordered pair (5, −6) is not a solution to the system because it makes at least one of the equations false. The ordered pair (5, −6) is a solution to the system because it makes both equations true.

Mathematics

2 answers:

aksik [14] · Answer 1 · 2022-08-27T08:25:15+03:00

Answer: The ordered pair (5,-6) is a solution to the first equation because it makes the first equation true.

The ordered pair (5,-6) is a solution to the second equation because it makes the second equation true.

Step-by-step explanation:

The given system of equations are :

$x+y=-1 ...(i)\\3x-y=21..(ii)$

In ordered pair (5, −6) , x -coordinate =5 and y-coordinate = -6

Put x= 5 and y=-6 in (i) , we get

$5+(-6)=-1\\\\\Rightarrow\ -1=-1$ , which is true.

That means (5,-6) is a solution to the first equation because it makes the first equation true.

Put x= 5 and y=-6 in (ii) , we get

$3(5)-(-6)=21\\\\\Rightarrow\ 15+6=21$

, which is true.

That means (5,-6) is a solution to the second equation because it makes the second equation true.

So , the correct statements are :

The ordered pair (5,-6) is a solution to the first equation because it makes the first equation true.
The ordered pair (5,-6) is a solution to the second equation because it makes the second equation true.

Likurg_2 [28] · Answer 2 · 2022-08-27T06:46:19+03:00

The correct options are:

The ordered pair (5, −6) is a solution to the first equation because it makes the first equation true.

The ordered pair (5, −6) is not a solution to the system because it makes at least one of the equations false.

Step-by-step explanation:

Given equations are:

$x+y=-1\\3x-y=21$

first of all we have to put the point in both equations to check if the point holds true on both equations

So,

Putting the point in the first equation

$x+y=-1\\5-6=-1\\-1=-1$

Putting the point in second equation

$3x-y=21\\3(5)-6=21\\15-6=21\\9\neq 21$

So,

The correct options are:

The ordered pair (5, −6) is a solution to the first equation because it makes the first equation true.

The ordered pair (5, −6) is not a solution to the system because it makes at least one of the equations false.

Keywords: Linear Equations, Solution

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