Question

Solve the system of equations by using the method of cross multiplication:
`1/x + 1/y = 7, 2/x + 3/y = 17`

Answer 1

Taking `1/x = u and 1/y` = v, the given equations become:
u + v = 7
2u + 3v = 17
The given equations may be written as:
u + v – 7 = 0 …..(i)
2u + 3v – 17 = 0 ……(ii)
Here, `a_1 = 1, b_1 = 1, c_1 = -7, a_2 = 2, b_2 = 3 and c_2 = -17`
By cross multiplication, we have:

`∴ u/([1×(−17) −3 ×(−7)]) = v/([(−7) × 2 −1 ×(−17)] )= 1/([3−2])`

`⇒u/((−17+21) )= v/((−14+17)) = 1/(1)`
`⇒u/4 = v/3 = 1/1`
`⇒u = 4/1 = 4, v = 3/1 = 3`
`⇒ 1/x = 4, 1/y = 3`
`⇒ x = 1/4, y = 1/3`

Hence, x = `1/4 and y = 1/3` is the required solution.