The pair of equations 2x + y = 5, 3x + 2y = 8 has

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A unique solution Explanation: 1. Identify coefficients Compare the given linear equations with the standard forms a1x + b1y = c1 and a2x + b2y = c2: First equation: 2x + y = 5 $\Rightarrow$ a1 = 2, b1 = 1, c1 = 5 Second equation: 3x + 2y = 8 $\Rightarrow$ a2 = 3, b2 = 2, c2 = 8 2. Compare ratios Calculate and compare the ratios of the coefficients of x and y: (a_1)/(a_2) = $\frac{2}{3}$ (b_1)/(b_2) = $\frac{1}{2}$ Since $\frac{2}{3}$ $\neq$ $\frac{1}{2}$, we have the condition: (a_1)/(a_2) $\neq$ (b_1)/(b_2) This condition dictates that the two lines intersect at exactly one point, meaning the system has one unique solution.

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