Question

find the value of x and y for the give pair of linear equations 14/2x+y + 3/2x-y = 5 and 3/2x+y - 4/2x-y = -25/7 where x≠0, y≠0 and y≠2x​

Answer 1

$\frac{14}{2x + y} + \frac{3}{2x - y} = 5$

$\frac{3}{2x + y} - \frac{4}{2x - y} = - \frac{25}{7}$

$let \: \frac{1}{2x + y} = a$

$let \: \frac{1}{2x - y} = b$

substituting the values of a and b

equation 1

$14a + 3b = 5$

equation 2

$3a - 4b = - \frac{25}{7}$

multiplying equation 1 by 4 and equation 2 by 3

$4(14a + 3b) = 4(5)$

$56a +12b = 20 \: ........(3)$

$3(3a - 4b) = 3( - \frac{25}{7} )$

$9a - 12b = - \frac{75}{7} \: ........(4)$

adding (1) and (2)

$65a = 20 + - \frac{75}{7} = \frac{65}{7}$

$a = \frac{1}{7}$

putting value of a in equation 1

$14 \times \frac{1}{7} + 3b = 5$

$b = 1$

$a = \frac{1}{2x + y} = \frac{1}{7}$

$2x + y = 7 \: .........(5)$

$b = \frac{1}{2x - y} = 1$

$2x - y = 1 \: .........(6)$

adding (5) and (6)

$4x = 8 \\ x = 2$

putting value of x in (5)

$2(2) - y = 1 \\ 4 - y = 1 \\ y = 3$

Thus, x=2 y=3