Solve the equations: 2x+1 3y + 2 3 ...
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Solve the equations: 2x+1 3y + 2 3 5 2(2x+1) 3(3y + 2) ON 5 ==-1

JEE/Engineering Exams
Maths
Solution
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Given equations are: ( frac{2 x+1}{3}+frac{3 y+2}{5}=2 ) and ( frac{2(2 x+1)}{3}-frac{3(3 y+2)}{5}=-1 ) Let ( frac{2 x+1}{3}=u ) and ( frac{3 y+2}{5}=v ) Then the equations become ( u+v=2 ) ( 2 u-3 v=-1 ) Multiplying (iii) by 3 , ( 3 u+3 v=6 ) Adding (iv) and (v), ( 5 u=5 Rightarrow u=1 ) Substituting this value of ( u ) in (iii), ( 1+v=2 Rightarrow v=2-1=1 ) Then ( frac{2 x+1}{3}=u=1 quad ) and ( quad frac{3 y+2}{5}=v=1 ) ( Rightarrow quad 2 x+1=3 quad ) and ( quad 3 y+2=5 ) ( Rightarrow quad 2 x=3-1=2 quad ) and ( quad 3 y=5-2=3 ) ( Rightarrow quad x=1 ) and ( quad y=1 )
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