Question

Solve the system of equations by using the method of cross multiplication:

`x/6 + y/15 - 4 = 0, x/3 - y/12 - 19/4 = 0`

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

`x/6 + y/15 = 4, x/3 - y/12 = 19/4`

Answer 1

The given equations may be written as:

`x/6 + y/15 - 4 = 0`   ...(i)

`x/3 - y/12 - 19/4 = 0`   ...(ii)

Here `a_1 = 1/6, b_1 = 1/15, c_1 = -4, a_2 = 1/3, b_2 = -1/12` and `c_2 = - 19/4`

By cross multiplication, we have:

∴ `x/([1/15 xx (-19/4) - (-1/12) xx (-4)]) = y/([(-4) xx 1/3 - (1/6) xx (-19/4)]) = 1/([1/6 xx (-1/12) xx 1/3 xx 1/15])`

⇒ `x/((-19/60 - 1/3)) = y/((-4/3 + 19/34)) = 1/((-1/72 - 1/45))`

⇒ `x/((-39/60)) = y/((-13/24)) = 1/((-13/360)`

⇒ `x = [(-39/60) xx (-360/13)] = 18, y = [(-13/24) xx (-360/13)] = 15`

Hence, x = 18 and y = 15 is the required solution.