Question

solve for X and Y : (b/a)x + (a/b)y = a^2+b^2; x+y=2ab​

Answer 1

Step-by-step explanation:

Given: System of equation

\frac{b}{a}x+\frac{a}{b}y=a^2+b^2

a

b

x+

b

a

y=a

2

+b

2

---------(1)

x+y=2abx+y=2ab -----------(2)

Using elimination method to solve for x and y

Multiply second equation by -b/a to eliminate x

-\frac{b}{a}x-\frac{b}{a}y=-\frac{b}{a}\cdot 2ab−

a

b

x−

a

b

y=−

a

b

⋅2ab

\frac{b}{a}x+\frac{a}{b}y=a^2+b^2

a

b

x+

b

a

y=a

2

+b

2

Add both equation to eliminate x

\frac{a}{b}y-\frac{b}{a}y=a^2+b^2-\frac{b}{a}\cdot 2ab

b

a

y−

a

b

y=a

2

+b

2

−

a

b

⋅2ab

y(\dfrac{a^2-b^2}{ab})=a^2-b^2y(

ab

a

2

−b

2

)=a

2

−b

2

y=aby=ab

Substitute y=ab into equation (2)

x+ab=2abx+ab=2ab

x=abx=ab

Hence, The solution of system of equation x=ab and y=ab

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