Question

1/2(2x+3y) +12/7(3x-2y) =1/2 and 7/2x+3y+4/3x-2y=2 the value of x&y? ​

Answer 1

Answer:

x = 5 and y = 1

Step-by-step explanation:

$\frac{1}{2(2x - 3y)} + \frac{12}{7(3x - 2y)} = \frac{1}{2} \: --- eq1$

$\frac{7}{2x + 3y} + \frac{4}{3x - 2y} = 2 \: \: - - - -eq2$

$let \: 2x - 3y \: be \: a \: and \: 3x - 2y \: be \: b$

Equation 1 becomes

$\frac{1}{2a} + \frac{12}{7b} = \frac{1}{2}$

$\frac{7b + 24a}{14ab} = \frac{1}{2}$

$14b + 48a = 14ab \: \: - - - eq3$

Equation 2 becomes

$\frac{7}{a} + \frac{4}{b} = 2$

$\frac{7b + 4a}{ab} = 2$

$7b + 4a = 2ab \: \: - - - eq4$

Multiplying equation 4 by 2 to solve equation 3 and 4 by elimination method, we get

14b+8a=4ab. as equation 4.

On solving, 14b gets eliminated from both the equations and we get

$40a = 10ab$

$40 = \frac{10ab}{a}$

$40 = 10b$

$b = 4$

Putting the value of b in equation 4, we get

$7 \times 4 + 4a = 2a \times 4$

$28 + 4a = 8a$

$28 = 4a$

$a = 7$

Now, a = 2x-3y and b = 3x-2y.

Putting the values of a and b, we get,

$7 = 2x - 3y \: \: - - - eq5$

$4 = 3x - 2y \: \: - - - eq6$

Solving equation 5 and 6 , we get x = 5 and y = 1