Question

Solve the following simultaneous equations
$\frac{1}{2}x-y=\frac{5}{2};x+\frac{1}{3}y=\frac{8}{3}$

Answer 1

$\frac{1}{2}x-y=\frac{5}{2}$ ....... $\left(1\right)$

or, $\frac{x-2y}{2}=\frac{5}{2}\Rightarrow x-2y=5$ ......... $\left(2\right)$

$x+\frac{1}{3}y=\frac{8}{3}$ ........... $\left(3\right)$

or, $\frac{3a+y}{3}=\frac{8}{3}\Rightarrow 3x+y=8$ .......... $\left(4\right)$

Solving $\left(2\right)$ and $\left(4\right)$

$3x-6y=15$

$3x+y=8$

_____________

$-7y=7$

$\therefore y=-1$

Putting $y=-1$ in $\left(2\right)$

$x-2(-1)=5$

or, $x=5/2=3$

$\therefore x=3$

$x=3,y=-1$