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) \( (-3,4) \)
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To solve these equations, we can substitute the ordered pairs into each equation to see which one satisfies them. For the equation \(2x + 3y = -10\), substituting the pair (1, -4) gives \(2(1) + 3(-4) = 2 - 12 = -10\); thus, (1, -4) is a solution to this equation. For the second equation \(-3x -5y = 1\), substituting (-3, 4) gives \(-3(-3) - 5(4) = 9 - 20 = -11\), which does not satisfy this equation. Now, checking the third equation \(-2x + y = 10\), substituting (1, -4) gives \(-2(1) + (-4) = -2 - 4 = -6\), not satisfied. However, substituting (-3, 4) gives \(-2(-3) + 4 = 6 + 4 = 10\), which satisfies this equation. In summary, (1, -4) solves the first equation, while (-3, 4) solves the second and third equations.