4x+6/y=15 and 6x-8/y=14 Hence find λ if y=λx-2
4x+$\frac{6}{y}$ =15 —(i)
6x-$\frac{8}{y}$=14 —(ii)
Multiplying Equation (i) by 4 and equation (ii) by 3 we get,
16x+$\frac{24}{y}$ = 60 —(iii)
18x-$\frac{24}{y}$=42 —-(iv)
Adding equation (iii) and (iv) we get,
16x+$\frac{24}{y}$ + 18x-$\frac{24}{y}$ =60+42
⟹ 34x = 102
⟹ x = $\frac{102}{34}$
⟹ x = 3
Now substituting the value of x in equation (i) we get,
4(3)+$\frac{6}{y}$ =15
⟹ 12 +$\frac{6}{y}$ =15
⟹ $\frac{6}{y}$ =15-12
⟹ $\frac{6}{y}$ = 3
⟹ 3y=6
⟹ y = $\frac{6}{3}$
⟹ y=2
∴ Required Solutions are , x= 3 and y =2
Now ,
y=λx-2
⟹ 2=3λ -2
⟹ 3λ = 2+2
⟹ 3λ =4
⟹ λ =$\frac{4}{3}$