Question

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)

Answer 1

D

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 )

Answer 2

`x = 4 \: and \: y = 0 \\`

D. (4,0)

Explanation:

`y - x = - 4 \\ - 4x - 6y = - 16 \\ \\ y = x - 4`

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

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

Since x=4, we can now find y:

`- 4x - 6y = - 16 \\ - 4(4) - 6y = - 16 \\ - 16 - 6y = - 16 \\ \\ ( - 6)/( - 6)y = ( - 16 + ( - 16))/( - 6) \\ \\ y = (0)/(6) \\ \\ y = 0`

Therefore (4,0) is the answer