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If x = 2 – α and y = 2 + α in a solution of 5x + 3y – 7 = 0 and x = 2β + 1 and y = β – 1 in a solution of 3x – 2y + 6 = 0 then find the value of α + β.

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Given equation = 5x + 3y – 7 = 0 

x = 2 – α and y = 2 + α 

∴ 5(2 – α) + 3(2 + α) – 7 = 0 

⇒ 10 – 5α+ 6 + 3α – 7 = 0 

⇒ 9 – 2α = 0 

⇒ 2α = 9 ⇒ α = 9/2 = 4.5 

Given equation 3x – 2y + 6 = 0 

x = 2β + 1 and y = β – 1 

∴ 3(2β + 1)- 2(β – 1) + 6 = 0 

⇒ 6β + 3 – 2β + 2 + 6 = 0

⇒ 4β + 11 = 0 ⇒ β = -11/4

∴ α + β = 9/2 - 11/4 = \(\frac {18-11}{4} = \frac {7}{4}\)

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