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Construct a consistent and independent system of equations that has ( − 1 , − 4 ) as its solution. Use x and y as your variables, and put your equations in the form A x + B y = C with A ≠ 0 and B ≠ 0 using the four answer boxes below. Note that there are many possible correct answers.

Respuesta :

amna04352

Answer:

x - y = 3

2x - y = 2

Step-by-step explanation:

x = 3 + y

2(3 + y) - y = 2

6 + 2y - y = 2

y = 2 - 6

y = -4

x = 3 + (-4)

x = 3 - 4

x = -1

Verified

MrRoyal

A consistent and independent system of equations has exactly one solution.

A possible system of equation is: [tex]\mathbf{-4x - 3y = 16}[/tex] and [tex]\mathbf{x -y =3}[/tex]

The solutions are given as:

[tex]\mathbf{(x,y) = (-1, -4)}[/tex]

The general equation is given as:

[tex]\mathbf{Ax + By = C}[/tex]

Substitute values for x and y

[tex]\mathbf{-A - 4B = C}[/tex]

Assume A = 1 and C = 3

So, we have:

[tex]\mathbf{-1 - 4B = 3}[/tex]

Collect like terms

[tex]\mathbf{- 4B = 3+1}[/tex]

[tex]\mathbf{- 4B = 4}[/tex]

Divide both sides by -4

[tex]\mathbf{B = -1}[/tex]

Substitute [tex]\mathbf{B = -1}[/tex], A = 1 and C = 3 in [tex]\mathbf{Ax + By = C}[/tex]

[tex]\mathbf{x -y =3}[/tex]

Also, we have:

[tex]\mathbf{-A - 4B = C}[/tex]

Assume A = -4 and C = 16

So, we have:

[tex]\mathbf{4 - 4B = 16}[/tex]

Collect like terms

[tex]\mathbf{- 4B = 16 - 4}[/tex]

[tex]\mathbf{- 4B = 12}[/tex]

Divide both sides by -4

[tex]\mathbf{B = -3}[/tex]

Substitute [tex]\mathbf{B = -3}[/tex], A = -4 and C = 16 in [tex]\mathbf{Ax + By = C}[/tex]

[tex]\mathbf{-4x - 3y = 16}[/tex]

Hence, a possible system of equation is:

[tex]\mathbf{-4x - 3y = 16}[/tex] and [tex]\mathbf{x -y =3}[/tex]

Read more about consistent and independent system of equations at:

https://brainly.com/question/16204664

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