Question

Solve for x and y
x-y/2=3 and x/2-2y/3=2/3​

Answer 1

$\sf \dfrac{x-y}{2}=3\\\\\to \sf x-y=6\\\\\to \sf x=6+y...(1)$

$\sf \dfrac{x}{2}-\dfrac{2y}{3}=\dfrac{2}{3}\\\\\to \sf \dfrac{3x-4y}{6}=\dfrac{2}{3}\\\\\to \sf 3x-4y=4\\\\\to \sf 3x=4+4y$

Sub. (1) here ,

$\to \sf 3(6+y)=4+4y\\\\\to \sf 18+3y=4+4y\\\\\to \sf \orange{y=14}\ \; \bigstar$

Sub. y value in (1) ,

$\to \sf x=6+(14)\\\\\to \sf \green{x=20}\ \; \bigstar$

Answer 2

Answer:

✡ Given ✡

$\leadsto$ $\dfrac{x-y}{2}$ = 3 ...... Equation no (1)

$\leadsto$ $\dfrac{x}{2}$ - $\dfrac{2y}{3}$ = $\dfrac{2}{3}$ ... Equation no (2)

✡ To Find ✡

$\leadsto$ The value of x and y.

✡ Solution ✡

$\dfrac{x-y}{2}$ = 3

$\implies$ x - y = 6

$\implies$ x = 6 + y ....... Equation no (1)

Again,

$\dfrac{x}{2}$ - $\dfrac{2y}{3}$ = $\dfrac{2}{3}$

$\implies$ $\dfrac{3x - 4y}{6}$ = $\dfrac{2}{3}$

$\implies$ 3x - 4y = 4

$\implies$ 3x = 4 + 4y .. Equation no (2)

▶ According to the question,

Substitute Equation no (1) we get,

$\implies$ 3(6 + y) = 4 + 4y

$\implies$ 18 + 3y = 4 + 4y

$\implies$ 3y - 4y = 4 - 18

$\implies$ y = $\text{\large\underline{\pink{14}}}$

Again, putting the value of y = 14 in the equation no (1) we get,

$\implies$ x = 6 + (14)

$\implies$ x = $\text{\large\underline{\green{20}}}$

$\therefore$ The value of x = 20 and y = 14.

Step-by-step explanation:

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