Question

Solve the system of equations by using the method of cross multiplication:
7x - 2y – 3 = 0,
`11x - 3/2 y – 8 = 0.`

Answer 1

The given equations may be written as:
7x - 2y – 3 = 0                   …….(i)
`11x - 3/2 y – 8 = 0`             …….(ii)
Here a1 = 7, b1 = -2, c1 = -3, a2 = 11, b2 = - `3/2` and c2 = -8
By cross multiplication, we have:

`∴ x/([(−2)×(−8) −(−32) ×(−3)]) = y/([(−3) × 11 −(−8) × 7])= 1/[(7 × (−32)−11 ×(−2)])`

`⇒x/((16− 9/2)) = y/((−33+56)) = 1/((−21/2 + 22))`

`⇒x/((23/2)) = y/23 = 1/((23/2))`

`⇒x = (23/2)/(23/2) = 1, y = 23/(23/2) = 2`

Hence, x = 1 and y = 2 is the required solution.