Sure! Let's find the solutions to the linear equation [tex]\(-x + 2y = 10\)[/tex] and complete the table as requested.
### Step-by-Step Solution:
1. When [tex]\(x = 0\)[/tex]:
Substitute [tex]\(x = 0\)[/tex] into the equation:
[tex]\[
-0 + 2y = 10 \implies 2y = 10 \implies y = \frac{10}{2} = 5
\][/tex]
So, [tex]\((x, y) = (0, 5)\)[/tex].
2. When [tex]\(x = 5\)[/tex]:
Substitute [tex]\(x = 5\)[/tex] into the equation:
[tex]\[
-5 + 2y = 10 \implies 2y = 10 + 5 \implies 2y = 15 \implies y = \frac{15}{2} = 7.5
\][/tex]
So, [tex]\((x, y) = (5, 7.5)\)[/tex].
3. When [tex]\(y = 0\)[/tex]:
Substitute [tex]\(y = 0\)[/tex] into the equation:
[tex]\[
-x + 2 \cdot 0 = 10 \implies -x = 10 \implies x = -10
\][/tex]
So, [tex]\((x, y) = (-10, 0)\)[/tex].
### Filled Table:
[tex]\[
\begin{array}{|c|c|c|}
\hline
x & y & (x, y) \\ \hline
0 & 5.0 & (0,5.0) \\ \hline
5 & 7.5 & (5,7.5) \\ \hline
-10 & 0 & (-10,0) \\ \hline
\end{array}
\][/tex]
This table represents the solutions to the equation [tex]\(-x + 2y = 10\)[/tex]:
[tex]\[
\begin{aligned}
&\left(0, 5.0\right) \\
&\left(5, 7.5\right) \\
&\left(-10, 0\right)
\end{aligned}
\][/tex]
