Question

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

3x + 2y + 25 = 0

2x + y + 10 = 0

Answer 1

The given system of equation is

3x + 2y + 25 = 0

2x + y + 10 = 0

Here

`a_1 = 3, b_1 = 2, c_1 = 25`

`a_2 = 2, b_2 = 1, c_2 = 10`

By cross-multiplication, we have

`=> x/(2xx 10-25xx 1) = (-y)/(3xx 10- 25xx 2) = 1/(3xx1 - 2xx2)`

`=> x/(20-25) = (-y)/(30-50) =- 1/(3-4)`

`=> x/(-5) = (-y)/(-20) = 1/(-1)`

Now `x/(-5) = 1/(-1)`

`=> x = (-5)/(-1) = 5`

And 

`(-y)/(-20) = 1/(-1)`

`=> y/20 = 1`

`=> y = -20`

Hence, x =  5, y = 20 is the solution of the given system of equations.