Question

Solve each of the following systems of equations by using the method of cross multiplication:
$1/x+1/y=7$
$2/x+3/y=17(x\ne 0andy\ne 0)$

Answer 1

Simplify given equations:

Let $1/x=u$ and $1/y=v$

$1/x+1/y=7$ implies

$u+v=7$

$2/x+3/y=17$ implies

$2u+3v=17$

New set of equation is:

$u+v=7...\left(1\right)$

$2u+3v=17...\left(2\right)$

From equation $\left(1\right):a_1=1,b_1=1$ and $c_1=-7$

From equation $\left(2\right):a_2=2,b_2=3$ and $c_2=-17$

Using cross multiplication method:

$\frac{u}{-17+21}=\frac{v}{-14+17}=\frac{1}{3-2}$

$\frac{u}{4}=1$ and $\frac{v}{3}=1$

$u=4$ and $q=3$

$x=1/4$ nad $y=1/3$ [Since we consider $p=1/x$ and $q=1/y$]

Answer $x=1/4,y=1/3$