Question

Solve the following system of equations by the method of cross-multiplication:

5ax + 6by = 28

3ax + 4by = 18

Answer 1

The given system of equation is

5ax + 6by = 28

`=> 5ax + 6by - 28 = 0` .....(i)

And 3ax + 4by - 18 = 0

`=> 3ax + 4by - 18 = 0` ....(ii)

Here

`a_1 = 5a, b_1 = 6b, c_1 = -28`

`a_2 = 3a,  b_2 = 4b, c_2 = -18`

By cross multiplication we have

`= x/(6b xx (-18) - (-28) xx 4b) = (-4)/(5a xx (-18) - (-28) xx 3a) = 1/(5a xx 4b - 6b xx 3a)`

`=> x/(-108b + 112b) = (-y)/(-90a + 80a) = 1/(20ab - 18ab)`

`=> x/(4b) = (-y)/(-6a) = 1/(2ab)`

Now

`x/(4b) = (-y)/(-6a) = 1/(2ab)`

Now

`x/(4b) = 1/(2ab)`

`=> x = (5b - 2a)/10ab`

And

`(-y)/(-6a) = 1/(2ab)`

`=> y = (6a)/(2ab) = 3/b`

Hence `x = 2/a, y = 3/b` is the solution of the given system of equations.