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If a set of equations are given as 3x−2y=5 and 3y−2x= 3 then find the value of (x +y)

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Detailed Solution

3x−2y=5 ------------------ (1)
3y−2x= 3 ------------------ (2)
From eqn (1),

3 x - 2 y = 5

3 x = 5 + 2 y

x = \frac{5 + 2 y}{3}

Substitute value for

x = \frac{5 + 2 y}{3}

in eqn (2)
3y−2x= 3

3 y - 2 (\frac{5 + 2 y}{3}) = 3

3 y - \frac{10 + 4 y}{3} = 3

\frac{9 y - 10 - 4 y}{3} = 3

9 y - 10 - 4 y = 9

5 y = 19

y = \frac{19}{5}

Substitute

y = \frac{19}{5} in eqn (1)

3 x - 2 y = 5

3 x - 2 (\frac{19}{5}) = 5

3 x - (\frac{38}{5}) = 5

3 x = 5 + (\frac{38}{5})

3 x = \frac{25 + 38}{5}

3 x = \frac{63}{5}

x = \frac{21}{5}

x + y = \frac{21}{5} + \frac{19}{5}

= \frac{21 + 19}{5} = \frac{40}{5} = 8

= \frac{40}{5} = 8

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