Questions: For each ordered pair, determine whether it is a solution to 5x - 8y = -29. (x, y) Is it a solution? ----------------------- Yes No (-3,1) ◯ 0 (0,-4) ◯ 0 (-9,-2) 0 0 (6,5) ◯ 0

Transcript text: For each ordered pair, determine whether it is a solution to $5 x-8 y=-29$. \begin{tabular}{|c|c|c|} \hline \multirow{2}{*}{$(x, y)$} & \multicolumn{2}{|c|}{ Is it a solution? } \\ \cline { 2 - 3 } & Yes & No \\ \hline$(-3,1)$ & $\bigcirc$ & 0 \\ \hline$(0,-4)$ & $\bigcirc$ & 0 \\ \hline$(-9,-2)$ & 0 & 0 \\ \hline$(6,5)$ & $\bigcirc$ & 0 \\ \hline \end{tabular}

Solution

Solution Steps

To determine whether each ordered pair $(x, y)$ is a solution to the equation $5x - 8y = -29$, substitute the values of $x$ and $y$ from each pair into the equation. If the equation holds true (i.e., both sides are equal), then the pair is a solution; otherwise, it is not.

Step 1: Evaluate the Pair $(-3, 1)$

Substituting $x = -3$ and $y = 1$ into the equation $5x - 8y$: \[ 5(-3) - 8(1) = -15 - 8 = -23 \neq -29 \] Thus, $(-3, 1)$ is not a solution.

Step 2: Evaluate the Pair $(0, -4)$

Substituting $x = 0$ and $y = -4$ into the equation: \[ 5(0) - 8(-4) = 0 + 32 = 32 \neq -29 \] Thus, $(0, -4)$ is not a solution.

Step 3: Evaluate the Pair $(-9, -2)$

Substituting $x = -9$ and $y = -2$ into the equation: \[ 5(-9) - 8(-2) = -45 + 16 = -29 \] Thus, $(-9, -2)$ is a solution.

Step 4: Evaluate the Pair $(6, 5)$

Substituting $x = 6$ and $y = 5$ into the equation: \[ 5(6) - 8(5) = 30 - 40 = -10 \neq -29 \] Thus, $(6, 5)$ is not a solution.

Final Answer

The only ordered pair that is a solution to the equation $5x - 8y = -29$ is $(-9, -2)$. Therefore, the answer is: \[ \boxed{(-9, -2)} \]

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