Question

solve the given eqation 8x+9y=42xy and 2x+3y=12xy

Answer 1

Hello,

it is a question from linear equation in two variables.
I am going to solve this sum by the method of elimination.

In this process we simply make any of the term equal in both the equations and by either adding or subtracting the two equations obtain the value of the remaining term.

So let's see the solution....

$8x + 9y = 42xy........(1) \\ 2x + 3y = 12xy......(2) \: \: \: \times 4 \\ \\ the \: equation \: becomes \\ 8x + 9y = 42xy \\ 8x + 12y = 48xy \\ \\ subtracting \: the \: two \: equations \\ (2) - (1) \\ \\ \\ 8x + 12y = 48xy \\ 8x + 9y = 42xy \\ - - - - - - - - - \\ 3y = 6xy \\ \\ so \: obtaining \: the \: values \\ y = \frac{6xy}{3} = 2xy \\ x = \frac{y}{2y} = \frac{1}{2} \\ \\ obtaining \: y \\ 8x + 9y = 42xy \\ 8 \times \frac{1}{2} + 9y = 42 \times \frac{1}{2} \times y \\ 4 + 9y = 21y \\ 21y - 9y = 4 \\ 12y = 4 \\ y = \frac{4}{12} = \frac{1}{3}$


So, the solution is
X=1/2
Y=1/3

Hope this will be helping you ✌️