Question

Solve the following equations:
$3x-2y=7$,
$xy=20$.

Answer 1

$3x-2y=\mathrm{7......}\left(i\right)xy=\mathrm{20..........}\left(ii\right)$

From $\left(ii\right)$
$y=\frac{20}{x}$

Substituting in $\left(i\right)$
$3x-\frac{40}{x}=73x^2-40=7x3x^2-7x-40=03x^2-15x+8x-40=03x(x-5)+8(x-5)=0(3x+8)(x-5)=0x=-\frac{8}{3},5$

Substituting in $\left(ii\right)$

For $x=-\frac{8}{3}$

$y=\frac{20}{-\frac{8}{3}}=-\frac{15}{2}$

For $x=5$

$y=\frac{20}{5}=4$

So the solutions of given equations are $x=5,-\frac{8}{3};y=4,-\frac{15}{2}$.