Question

Solve for x and y:

${\displaystyle x+\frac{6}{y}=6,3x-\frac{8}{y}=5}$

Answer 1

The given equations are:
x + ${\displaystyle \frac{6}{y}}$ = 6 ……..(i)
3x - ${\displaystyle \frac{8}{y}}$ = 5 ……..(ii)
Putting ${\displaystyle \frac{1}{y}}$ = v, we get:
x + 6v = 6 …….(iii)
3x – 8v = 5 ……(iv)
On multiplying (iii) by 4 and (iv) by 3, we get:
4x + 24v = 24 ……..(v)
9x – 24v = 15 ……..(vi)
On adding (v) from (vi), we get:
13x = 39 ⇒ x = 3
On substituting x = 3 in (i), we get:
3 + ${\displaystyle \frac{6}{y}}$ = 6
⇒${\displaystyle \frac{6}{y}}$ = (6 – 3) = 3 ⇒ 3y = 6 ⇒ y = 2
Hence, the required solution is x = 3 and y = 2.