Question

Solve for x and y:
(x+1)/2+ (y-1)/3= 9; (x-1)/3+(y+1)/2=8

Answer 1

xy-x+y=55 & xy+x-y=49 ... solving these equations you get the ans.. :-)

Answer 2

$\frac{x-1}{2} + \frac{y-1}{3}=9$

Taking L.C.M. of denominators of both the fractions i.e. 6.

$\frac{3(x+1)+2(y-1)}{6}=9$

Transferring 6 in R.H.S.

$3x+3+2y-2=54$

$3x+2y=53 --------eq(1)$

$\frac{x-1}{3} + \frac{y+1}{2} = 8$

Taking L.C.M. of denominators of both the fractions i.e. 6.

$\frac{2(x-1)+3(y+1)}{6} = 8$

$2X-2+3Y+3=48$

$2x+3y=47 ------eq(2)$

Solving eq (1) and eq (2) by multiplying eq (1)*2 and eq (2)*3

$6x+9y=141 ------[eq(2)*3]$
$6x+4y=106 ------[eq(1)*2]$

⇒$5y=35$$So, y=7$

Hence, Putting y=7 in eq(1)

$3x+14=53$

$3x=53-14$

$x= \frac{39}{3}$

$x=13$

x=13 , y=7
In this way we get the answer of these type of problems.