To find solutions for the equation [tex]\(8x + 4y = 24\)[/tex], we'll determine the intercepts where the line intersects the x-axis and y-axis.
### Step-by-Step Solution:
1. Finding the y-intercept:
- The y-intercept occurs when [tex]\(x = 0\)[/tex].
- Substitute [tex]\(x = 0\)[/tex] into the equation [tex]\(8x + 4y = 24\)[/tex]:
[tex]\[
8(0) + 4y = 24
\][/tex]
[tex]\[
4y = 24
\][/tex]
[tex]\[
y = 6
\][/tex]
- Therefore, the y-intercept is [tex]\(y = 6\)[/tex]. Thus, the ordered pair when [tex]\(x = 0\)[/tex] is [tex]\((0, 6)\)[/tex].
2. Finding the x-intercept:
- The x-intercept occurs when [tex]\(y = 0\)[/tex].
- Substitute [tex]\(y = 0\)[/tex] into the equation [tex]\(8x + 4y = 24\)[/tex]:
[tex]\[
8x + 4(0) = 24
\][/tex]
[tex]\[
8x = 24
\][/tex]
[tex]\[
x = 3
\][/tex]
- Therefore, the x-intercept is [tex]\(x = 3\)[/tex]. Thus, the ordered pair when [tex]\(y = 0\)[/tex] is [tex]\((3, 0)\)[/tex].
### Filling Out the Table:
Now that we have both intercepts, we can complete the table:
[tex]\[
\begin{array}{|l|l|l|}
\hline
x & y & \text{Ordered Pair} \\
\hline
0 & 6 & (0, 6) \\
\hline
3 & 0 & (3, 0) \\
\hline
\end{array}
\][/tex]
So, the two answers are the ordered pairs [tex]\((0, 6)\)[/tex] and [tex]\((3, 0)\)[/tex].
