Solve: 4x+6/y=15 and 6x-8/y=14 Hence find λ if y=λx-2

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 =$\frac{4}{3}$

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