Question

Solve the following simultaneous equation
$\frac{27}{x-2}+\frac{31}{y+3}=85$
$\frac{31}{x-2}+\frac{27}{y+3}=89$

Answer 1

$\frac{27}{x-2}+\frac{31}{y+3}=85$ ...... (1)
$\frac{31}{x-2}+\frac{27}{y+3}=89$ ...... (2)
Substituting $\frac{1}{x-2}=m$ and $\frac{1}{y+3}=n$ in the above equations
We get
$27m+31n=85$ ....... (3)
$31m+27n=89$ ....... (4)
Multiplying equation (3) by 31 and equation (4) by 27, we get
$837m+961n=2635$
$837m+729n=2403$
- - -
..............................
$232n=232$
$n=1$
Substituting $n=1$ in equation (3), we get
$27m+31=85$
$27m=54$
$m=2$
Resubstituting the values of m and n, we get
$\frac{1}{x-2}=2$ and $\frac{1}{y+3}=1$
$1=2(x-2)\therefore y+3=1$
$2x-4=1$ $y=-2$
$2x=5$
$x=\frac{5}{2}$