Solve the following two variable Linear equation $\frac{4}{A} + \frac{3}{B} = 8,\frac{6}{A} - \frac{4}{B} = 5$

Home » Solve the following two variable Linear equation

Solve the following two variable Linear equation $\frac{4}{A} + \frac{3}{B} = 8,\frac{6}{A} - \frac{4}{B} = 5$

Taking $1/A=u$

Then the two equation becomes,

$4u+3B=8$ …………………… (i)

$6u-4B=-5$ ……………………. (ii)

From (i), we get

$\begin{array}{l} 4u = 8 - 3B\\ u = (8 - 3B)/4 \end{array}$ …….. (iii)

Substituting u in (ii)

$\begin{array}{l} [6(8 - 3B)/4] - 4B = - 5\\ [3(8 - 3B)/2] - 4B = - 5\\ 249B - 8B = - 5A2\\ 24 - 17B = - 10\\ - 17B = - 34\\ B = 2 \end{array}$

Putting B=2 in (iii) we get,

$\begin{array}{l} u = (8 - 3(2))/4\\ u = (8 - 6)/4\\ u = 2/4 = 1/2\\ A = 1/u = 2\\ A = 2 \end{array}$

So, the solution of the pair of equations given is $A=2$ and $B=2$ .

i

Sign up now and study all subjects for free