Question

x/3+y/2= 8 3x/4-y/4=7​

Answer 1

Answer:

x=12 & y=8

Step-by-step explanation:

x/3+y/2= 8

Multiplying both sides by 6 (LCM of 3 & 2), we get

2x+3y=48 ....... eqn 1

3x/4-y/4=7

Multiplying both sides by 4,  we get​

3x-y=28 ....... eqn 2

Multiplying eqn 2 by 3 and adding it to eqn 1, we get

9x-3y=84

2x+3y=48

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11x=132

or x=132/11=12

Substituting this value in eqn 2, we get

3x-y=28

3×12-y=28

or y=36-28=8

∴ x=12 & y=8

Answer 2

Given,

$\rm \frac{x}{3} + \frac{y}{2} = 8 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \cdots(1) \\ \\ \rm \frac{3x}{4} - \frac{y}{4} = 7\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \cdots(2)$

Simplifying the (above)equations,

$\to \rm \frac{2x + 3y}{6} = 8 \\ \to \bf2x + 3y = 48 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \cdots( \tt{}a)$

And,

$\to \rm \frac{3x - y}{4} = 7 \\ \to \bf3x - y = 28\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \cdots(b)$

From Equation b, we have,

$\bf{}y = 3x - 28 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \cdots(p)$

Putting Equation p in Equation a, we get,

$\to \tt2x + 3(3x - 28) = 48 \\ \to \tt2x + 9x - 84 = 48 \\ \to \tt11x - 84 = 48 \\ \to \tt \: \: \: \: 11x = 48 + 84\\ \to \tt \: \: \: \: 11x = 132 \\ \\ \to \tt \frac{11x}{11} = \frac{132}{11} \\ \\ \to \tt \: \: \: \: \: x = 12$

Putting the obtained value of x in Equation p, we get,

$\rm{}y = 3x - 28 \\ \rm{} y = 3(12) - 28 \\ \rm{} y = 36 - 28 \\ \rm{}y = 8$

Hence,

• x = 8 & y = 12