Question

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

`1/x + 1/y = 7, 2/x + 3/y = 17`

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

`1/x + 1/y = 7, 2/x + 3/y = 17 (x ≠ 0, y ≠ 0)`

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, a₁ = 1, b₁ = 1, c₁ = –7, a₂ = 2, b₂ = 3 and c₂ = –17

By cross multiplication, we have:

∴ `u/([1 xx (-17) - 3 xx (-7)]) = v/([(-7) xx 2 - 1 xx (-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.