QuestionFind ordered pairs $(x, y)$ that satisfy $8x + 2y = 24$ . Create a table to display them.

Studdy Solution

STEP 1

Assumptions1. We are creating a table of ordered pairs $(x, y)$ that satisfy the equation $8x +y =24$ . . We will choose values for $x$ and solve for $y$ to create the ordered pairs.

STEP 2

First, let's rearrange the equation to solve for $y$ in terms of $x$ .
$8x +2y =24$ Subtract $8x$ from both sides to isolate $y$ .
$2y =24 -8x$ Then divide by2 to solve for $y$ .
$y = \frac{24 -8x}{2}$

STEP 3

Now we can choose values for $x$ and calculate the corresponding $y$ values.
Let's start with $x =0$ . Substitute $x =0$ into the equation for $y$ .
$y = \frac{24 -8(0)}{2}$

STEP 4

Calculate the value of $y$ when $x =0$ .
$y = \frac{24}{2} =12$ So the ordered pair when $x =0$ is $(0,12)$ .

STEP 5

Next, let's choose $x =1$ . Substitute $x =1$ into the equation for $y$ .
$y = \frac{24 -8(1)}{2}$

STEP 6

Calculate the value of $y$ when $x =1$ .
$y = \frac{24 -8}{2} =8$ So the ordered pair when $x =1$ is $(1,8)$ .

STEP 7

Continue this process for several more values of $x$ . For example, let's choose $x =2$ .
Substitute $x =2$ into the equation for $y$ .
$y = \frac{24 -(2)}{2}$

STEP 8

Calculate the value of $y$ when $x =2$ .
$y = \frac{24 -16}{2} =4$ So the ordered pair when $x =2$ is $(2,4)$ .

STEP 9

Finally, let's choose $x =3$ . Substitute $x =3$ into the equation for $y$ .
$y = \frac{24 -8(3)}{2}$

STEP 10

Calculate the value of $y$ when $x =3$ .
$y = \frac{24 -24}{2} =0$ So the ordered pair when $x =3$ is $(3,0)$ .

STEP 11

Now we can fill in the table with the ordered pairs we found.
\begin{tabular}{||c || c | c||} \hline x & y & Ordered Pair \\ [0.5ex] \hline\hline0 & & (0,) \\ \hline &8 & (,8) \\ \hline &4 & (,4) \\ \hline3 &0 & (3,0) \\ \hline\end{tabular}

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