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For the equation [tex]-3x + 2y = -6[/tex]:

a) Complete the table:
\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
& \\
\hline
& \\
\hline
0 & \\
\hline
\end{tabular}



Answer :

GinnyAnswer
To complete the table for the equation [tex]\(-3x + 2y = -6\)[/tex], we will determine the corresponding [tex]\(y\)[/tex] values for given [tex]\(x\)[/tex] values. We need to find the [tex]\(y\)[/tex] values for [tex]\(x = -3\)[/tex], [tex]\(x = -1\)[/tex], and [tex]\(x = 0\)[/tex].

Here's how we do this step by step:

1. For [tex]\(x = -3\)[/tex]:

[tex]\[ -3(-3) + 2y = -6 \\ 9 + 2y = -6 \\ 2y = -6 - 9 \\ 2y = -15 \\ y = \frac{-15}{2} \\ y = -7.5 \][/tex]

2. For [tex]\(x = -1\)[/tex]:

[tex]\[ -3(-1) + 2y = -6 \\ 3 + 2y = -6 \\ 2y = -6 - 3 \\ 2y = -9 \\ y = \frac{-9}{2} \\ y = -4.5 \][/tex]

3. For [tex]\(x = 0\)[/tex]:

[tex]\[ -3(0) + 2y = -6 \\ 0 + 2y = -6 \\ 2y = -6 \\ y = \frac{-6}{2} \\ y = -3.0 \][/tex]

Now let's complete the table with the calculated values:

\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
-3 & -7.5 \\
\hline
-1 & -4.5 \\
\hline
0 & -3.0 \\
\hline
\end{tabular}

So, the completed table is:
\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
-3 & -7.5 \\
\hline
-1 & -4.5 \\
\hline
0 & -3 \\
\hline
\end{tabular}

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