Question

x/2+y/3=1 x/3+y/2=1​

Answer 1

Answer:

x = 6/5

y = 6/5

Step-by-step explanation:

Given,

x/2 + y/3 = 1 ----- (i)

x/3 + y/2 = 1​ ----- (ii)

Equating (i) and (ii),

x/2 + y/3 = x/3 + y/2

(3x + 2y)/6 = (2x + 3y)/6

3x + 2y = 2x + 3y

x = y ----- (iii)

Substituting the value of x in (i)

y/2 + y/3 = 1

(3y + 2y)/6 = 1

5y = 6

y = 6/5

x = 6/5

Answer 2

Value of x and y is 6/5.

Given:

• $\frac{x}{2} + \frac{y}{3} = 1$
• $\frac{x}{3} + \frac{y}{2} = 1$

To find:

• Value of x and y.

Solution:

Step 1:

Take LCM of both equations

$\frac{3x + 2y}{6} = 1$

or

$\bf 3x + 2y = 6 ...eq1$

and

$\frac{2x + 3y}{6} = 1$

or

$\bf 2x + 3y = 6 ...eq2$

Step 2:

Add both equations.

$\bf 5x + 5y = 12...eq3$

Subtract both equations.

$\bf x - y = 0...eq4$

Step 3:

Multiply eq4 by 5 and both eq3 and 4

$5x + 5y = 12 \\ 5x - 5y = 0 \\ - - - - - - - \\ 10x = 12$

or

$x = \frac{12}{10}$

or

$\bf x = \frac{6}{5}$

Put value of x in eq4 and find Value of y.

$\frac{6}{5} - y = 0$

or

$\bf y = \frac{6}{5}$

Thus,

Values of x and y are same and equal to 6/5.

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