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For what value of a do $2 x + 3 y = 7$ and $(a - 1) x + (a + 2) y = 3 a$ have infinitely many solutions?

Competition practiceAlgebra

A7
B3
C5
D1/7

Step-by-Step Solution

Need

(a - 1) /2 = (a + 2) /3 = 3 a /7

. The first equality gives

3 a - 3 = 2 a + 4

, so

a = 7

; then each ratio equals 3.

Answer: A) 7

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