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3. Which ordered pair is a solution to the system of linear equation below?

y - x= -4
-4x – 6y= -16

A. (0,-4)
B. (-4,0)
C. (0,4)
D. (4,0)

Respuesta :

Answer:

D

Step-by-step explanation:

y - x = - 4 ( add x to both sides )

y = x - 4 → (1)

- 4x - 6y = - 16 → (2)

substitute y = x - 4 into (2)

- 4x - 6(x - 4) = - 16

- 4x - 6x + 24 = - 16

- 10x + 24 = - 16 ( add 24 to both sides )

- 10x = - 40 ( divide both sides by - 10 )

x = 4

substitute x = 4 into (1)

y = 4 - 4 = 0

solution is (4, 0 )

shanshancupcake

Answer:

[tex]x = 4 \: and \: y = 0 \\ [/tex]

D. (4,0)

Step-by-step explanation:

[tex]y - x = - 4 \\ - 4x - 6y = - 16 \\ \\ y = x - 4[/tex]

since y is x-4, we can substitute it into the second equation

[tex] - 4x - 6(x - 4) = - 16 \\ - 4x - 6x + 24 = - 16 \\ - 10x + 24 = - 16 \\ - 10x = - 16 - 24 \\ - 10x = - 40 \\ \frac{ - 10} {- 10} x = \frac{ - 40}{ - 10} \\ \\ x = 4[/tex]

Since x=4, we can now find y:

[tex]- 4x - 6y = - 16 \\ - 4(4) - 6y = - 16 \\ - 16 - 6y = - 16 \\ \\ \frac{ - 6}{ - 6}y = \frac{ - 16 + ( - 16)}{ - 6} \\ \\ y = \frac{0}{6} \\ \\ y = 0 [/tex]

Therefore (4,0) is the answer

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