Question

for the following equation, determine the values of the missing entries. reduce all fractions to lowest terms. 12x - 8y = 16 note: each column in the table represents an ordered pair. if multiple solutions exist, you only need to identify one.

Answer 1

Given an equation 12x - 8y = 16 .

We have complete the table given in the question.

Now, at y = 0.

`\begin{gathered} 12x-8(0)=16 \\ 12x=16 \\ x=(16)/(12) \\ x=(4)/(3) \end{gathered}`

Thus, the first box fills with 4/3.

at x = 0.

`\begin{gathered} 12(0)-8y=16 \\ -8y=16 \\ y=-2 \end{gathered}`

Thus, the second box fills with -2.

at x = 2.

`\begin{gathered} 12(2)-8y=16 \\ 24-8y=16 \\ -8y=16-24 \\ -8y=-8 \\ y=1 \end{gathered}`

Thus, the third box fills with 1.

at y = 4.

`\begin{gathered} 12x-8(4)=16 \\ 12x-32=16 \\ 12x=16+32 \\ 12x=48 \\ x=(48)/(12) \\ x=4 \end{gathered}`

Thus, the fourth box fills with 4.