Question

Solve : -
x/5 + y/6 + 1 = x/6 + y/5 = 28

Answer 1

$\frac{x}{5} + \frac{y}{6} + 1 = \frac{x}{6} + \frac{y}{5} = 28$

$\frac{x}{5} + \frac{y}{6} + 1 = 28 \rightarrow equation \: \: 1$

$\frac{x}{6} + \frac{y}{5} = 28 \rightarrow equation \: \: 2$

Simplifying equation 1:

L.C.M of denominators of equation 1 = L.C.M of 5,6 and 1 = 30.

$\frac{x \times 6}{5 \times 6} + \frac{y \times 5}{6 \times 5} + \frac{1 \times 30}{1 \times 30} = 28 \\ \\ \implies \frac{6x + 5y + 30}{30} = 28 \\ \\ \implies 6x + 5y + 30 = 28 \times 30 \\ \\ \implies 6x + 5y = 840 - 30 = 810$

Simplifying equation 2:

L.C.M of denominators of equation 2 = L.C.M of 6 and 5 = 30.

$\frac{x \times 5}{6 \times 5} + \frac{y \times 6}{5 \times 6} = 28 \\ \\ \implies \frac{5x + 6y}{30} = 28 \\ \\ \implies 5x + 6y = 28 \times 30 = 840$

Multiplying equation 1 by 5 and equation 2 by 6 to eliminate y:

Equation 1:

36x + 30y = 810 * 6 = 4860

Equation 2:

25x + 30y = 840 * 5 = 4200

Equation 1 - Equation 2:

36x + 30y = 4860

-25x - 30y = -4200

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11x = 660

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$x = \frac{660}{11}$

x = 60.

Substituting the value of x in equation 1:

$6(60) + 5y = 810 \\ 360 + 5y = 810 \\ 5y = 810 - 360 \\ 5y = 450 \\ y = \frac{450}{5} \\ y = 90$

Therefore, x = 60 and y = 90 are the solutions to the given equation.

Answer 2

Answer:-

$(x/5 + y/6 = 27 )$

$(x / 6 + y / 5 = 28)$

Now we should multiply theses Equations with 30

$(6x + 5y = 810 )$

$(5x + 6y = 840 )$

Now we should multiply this third equation with 6

$(36x + 30y = 4860)$

Now, Multiplying equation 5

$(25x + 30y = 4200)$

$(11x = 660)$

$(x = 660 / 11)$

$(x = 60)$

$(y = 90)$

$Hence \: answer \: x = 60 \: and \: y = 90$