Question

Solve each of the following systems of equations by the method of cross-multiplication :

x + 2y + 1 = 0
2x − 3y − 12 = 0

Answer 1

The given system of equation is

x + 2y + 1 = 0

2x − 3y − 12 = 0

Here

`a_1 = 1, b_1 = 2, c_1 = 1`

`a_2 = 2, b_2 = -3, c_3 = -12`

By cross-multiplication, we get

`=> x/(2xx(-12)-1xx(-3)) = (-y)/(1 xx (-12) - 1 xx 2) = 1/(1xx (-3) - 2xx2)`

`=> x/(-24 + 3) = (-y)/(-12 - 2) = 1/(-3-4)`

`=> x/(-21) = (-y)/(-14) = 1/(-7)`

Now

`x/(-21) = 1/(-7)`

`=> x = (-21)/7 = 3`

and 

`(-y)/(-14) = 1/-7`

`=> y/14 = (-1)/7`

`=> y = (-14)/7 = -2`

Hence, the solution of the given system of equations is x = 3 and y = -2