Questions: Lines and Functions Identifying solutions to a linear equation in two variables For each ordered pair, determine whether it is a solution to (x=-9). ((x, y)) Is it a solution? ------ ((0,6)) ◯ ◯ ((-7,1)) ◯ ◯ ((4,-9)) ◯ ◯ ((-9,-3)) ◯ ◯

Lines and Functions Identifying solutions to a linear equation in two variables For each ordered pair, determine whether it is a solution to (x=-9). ((x, y)) Is it a solution? ------ ((0,6)) ◯ ◯ ((-7,1)) ◯ ◯ ((4,-9)) ◯ ◯ ((-9,-3)) ◯ ◯
Transcript text: Lines and Functions Identifying solutions to a linear equation in two variables For each ordered pair, determine whether it is a solution to $x=-9$. \begin{tabular}{|c|c|c|} \hline \multirow{2}{*}{$(x, y)$} & \multicolumn{2}{|c|}{ Is it a solution? } \\ \cline { 2 - 3 }$(0,6)$ & $\bigcirc$ & $\bigcirc$ \\ \hline$(-7,1)$ & $\bigcirc$ & $\bigcirc$ \\ \hline$(4,-9)$ & $\bigcirc$ & $\bigcirc$ \\ \hline$(-9,-3)$ & $\bigcirc$ & $\bigcirc$ \\ \hline \end{tabular}
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Solution

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Solution Steps

To determine whether each ordered pair \((x, y)\) is a solution to the equation \(x = -9\), we need to check if the \(x\)-coordinate of each pair is equal to \(-9\). If it is, then the pair is a solution; otherwise, it is not.

Step 1: Identify the Equation

The given equation is \(x = -9\).

Step 2: Evaluate Each Ordered Pair

We need to check if the \(x\)-coordinate of each ordered pair is equal to \(-9\).

Step 3: Check Each Pair

  1. For \((0, 6)\):

    • \(x = 0\)
    • \(0 \neq -9\)
    • Therefore, \((0, 6)\) is not a solution.

  2. For \((-7, 1)\):

    • \(x = -7\)
    • \(-7 \neq -9\)
    • Therefore, \((-7, 1)\) is not a solution.

  3. For \((4, -9)\):

    • \(x = 4\)
    • \(4 \neq -9\)
    • Therefore, \((4, -9)\) is not a solution.

  4. For \((-9, -3)\):

    • \(x = -9\)
    • \(-9 = -9\)
    • Therefore, \((-9, -3)\) is a solution.

Final Answer

\[ \begin{array}{|c|c|} \hline (x, y) & \text{Is it a solution?} \\ \hline (0, 6) & \boxed{\text{False}} \\ \hline (-7, 1) & \boxed{\text{False}} \\ \hline (4, -9) & \boxed{\text{False}} \\ \hline (-9, -3) & \boxed{\text{True}} \\ \hline \end{array} \]

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