Match the equation on the left with the appropriate ordered pair solution on the right. \[ \begin{array}{l} 2 x+3 y=-10 \\ -3 x-5 y=1 \\ -2 x+y=10 \end{array} \] (1, -4) \( (-3,4) \)

Let's determine which ordered pair \((x, y)\) satisfies each equation by substituting the values into the equations. ### Given Ordered Pairs: 1. \((1, -4)\) 2. \((-3, 4)\) ### Equations: 1. \(2x + 3y = -10\) 2. \(-3x - 5y = 1\) 3. \(-2x + y = 10\) --- ### **1. \(2x + 3y = -10\)** - **Substitute \((1, -4)\):** \[ 2(1) + 3(-4) = 2 - 12 = -10 \quad \checkmark \] - **Substitute \((-3, 4)\):** \[ 2(-3) + 3(4) = -6 + 12 = 6 \neq -10 \quad \text{✗} \] **Conclusion:** \((1, -4)\) satisfies this equation. --- ### **2. \(-3x - 5y = 1\)** - **Substitute \((1, -4)\):** \[ -3(1) - 5(-4) = -3 + 20 = 17 \neq 1 \quad \text{✗} \] - **Substitute \((-3, 4)\):** \[ -3(-3) - 5(4) = 9 - 20 = -11 \neq 1 \quad \text{✗} \] **Conclusion:** Neither \((1, -4)\) nor \((-3, 4)\) satisfies this equation. --- ### **3. \(-2x + y = 10\)** - **Substitute \((1, -4)\):** \[ -2(1) + (-4) = -2 - 4 = -6 \neq 10 \quad \text{✗} \] - **Substitute \((-3, 4)\):** \[ -2(-3) + 4 = 6 + 4 = 10 \quad \checkmark \] **Conclusion:** \((-3, 4)\) satisfies this equation. --- ### **Final Matching:** - **\(2x + 3y = -10\)** matches with **\((1, -4)\)** - **\(-2x + y = 10\)** matches with **\((-3, 4)\)** The equation \( -3x - 5y = 1 \) has **no matching ordered pair** among the given options. **Summary:** \[ \begin{align*} 2x + 3y &= -10 &\leftrightarrow&\ (1,\ -4) \\ -2x + y &= 10 &\leftrightarrow&\ (-3,\ 4) \\ -3x - 5y &= 1 &\leftrightarrow&\ \text{No match} \end{align*} \]