Question

Solve each of the following systems of equations by the method of cross-multiplication:
x/a = y/b,
ax + by = a² + b²

Answer 1

Answer:

The value of x is a ,

The value of y is b

Step-by-step explanation:

Given as :

The two linear equation area

$\dfrac{x}{a}$   =  $\dfrac{y}{b}$                 .......1

Or, x = $\dfrac{ay}{b}$           ( by cross multiplication )

And

a x + b y = a² + b²             ......2

Put the value of x into eq 2

∵ a × ( $\dfrac{ay}{b}$ ) + b y = a² + b²  

Taking LCM , we get

Or, a² y + b² y = b (  a² + b²  )      

Or, y ( a² + b²  )  =  b (  a² + b²  )      

∴   y =     $\dfrac{b (a^{2}+b^{2})}{(a^{2}+b^{2})}$

removing numerator and denominator common terms

i.e,   y = b

So, The value of y = b

Put the value of y in x = $\dfrac{ay}{b}$

we get ,    x = $\dfrac{a\times b}{b}$

removing numerator and denominator common terms

i.e    x = a

So, The value of x = a

Hence, The value of x is a , and The value of y is b    Answer