Find the value of alpha and beta for which the following pair of linear equations have infinite number of solutions: 2x +3y=7 ; 2 (alpha beta)x + (alpha+ beta) y = 28.
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Given pair of equations 2x + 3y = 7 and 2αx + (α + β )y = 28 If pair of equations have infinite many solutions then a1 / a2 = b1 / b2 = c1 / c2 . a1 = 2 a2 = 2α , b1 = 3 ,b2 = (α + β ) ,c1 = 7 ,c2 = 28 1 / α = 3 / (α + β ) = 7 / 28 1 / α = 7 / 28 ⇒ α = 4 α = 4 ---------(1) and 3 / (α + β ) = 7 / 28 (α + β ) = 12 ---------(2) from Equations (1) and (2) we get β = 8.
Hope it helpful
Given pair of equations 2x + 3y = 7 and 2αx + (α + β )y = 28 If pair of equations have infinite many solutions then a1 / a2 = b1 / b2 = c1 / c2 . a1 = 2 a2 = 2α , b1 = 3 ,b2 = (α + β ) ,c1 = 7 ,c2 = 28 1 / α = 3 / (α + β ) = 7 / 28 1 / α = 7 / 28 ⇒ α = 4 α = 4 ---------(1) and 3 / (α + β ) = 7 / 28 (α + β ) = 12 ---------(2) from Equations (1) and (2) we get β = 8.
Hope it helpful
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