Question

X + 6/y = 6 , 3x - 8/y = 5

Answer 1

X+6/y = 6
X = 6 - 6/y

3x - 8/y = 5
3(6 - 6/y) - 8/y = 5
18 - 18/y - 8/y = 5
-26/y = 5 - 18
-26/y = - 13
Y = - 26/-13
Y = 2

X = 6 - 6/2
X = 6 - 3
X = 3

Answer 2

The value of (x, y) is (3, 2)

The given two equations are  

$x+\frac{6}{y}=6 \rightarrow(1)$

$3 x-\frac{8}{y}=5 \rightarrow(2)$

The given two equations can be solved using substitution method  

Equation (1) can be written as  

$\frac{1}{y}=\frac{1}{6}(6-x) \rightarrow(3)$

Substituting equation (3) in equation (2)

$3 x-\frac{8}{y}=5$

$3 x-\frac{1}{y}(8)=5$

$3 x-8\left(\frac{1}{6}(6-x)\right)=5$

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

$3 x+\frac{8 x}{6}=13$

$18 x+8 x=78$

$26x=78$

$x=\frac{78}{26}$

x = 3

Substituting the value of x in equation (3)

$\frac{1}{y}=\frac{1}{6}(6-x)=\frac{1}{6}(6-3)=\frac{1}{6} \times 3=\frac{1}{2}$

$\frac{1}{y}=\frac{1}{2}$

Therefore y = 2  

Hence the value of (x, y) is (3, 2).