Question

xa-yb=2 ax-by=a2-b2
​

Answer 1

Step-by-step explanation:

*Given:

$\frac{x}{a} + \frac{y}{b} = 2...eq1 \\ \\ ax - by = {a}^{2} - {b}^{2}...eq2$

To find: Solve given linear equations

Solution:

Step 1: Take LCM and simplify eq1

$\frac{x}{a} + \frac{y}{b} = 2 \\ \\ \frac{bx +ay}{ab} = 2 \\ \\ or \\ \\ bx +ay = 2ab...eq3$

Step 2: Multiply eq3 by a and eq2 by b and subtract both

$abx+{a}^{2} y = 2 {a}^{2} b \\ abx - {b}^{2} y = {a}^{2}b - {b}^{3} \\ ( - ) \: \: \: \: \: \:\: ( + ) \: \: \: \: ( - ) \: \: \: \: \: \: \: \: \: \: \: \: \\ - - - - - - - - - - \\ ( {a}^{2} + {b}^{2} )y = 2 {a}^{2} b - {a}^{2} b + {b}^{3} \\ \\ y = \frac{ {a}^{2}b + {b}^{3} }{ {a}^{2} + {b}^{2} } \\ \\ y = \frac{b( {a}^{2} + {b}^{2}) }{( {a}^{2}+ {b}^{2} ) }\\\\y=b$

Step 3: Put the value of y in eq2

$ax -b^{2} = {a}^{2} - {b}^{2} \\ \\ ax = {a}^{2} - {b}^{2} +b^{2} \\ \\ ax = a^2 \\ \\ x = \frac{ {a}^{2}}{a} \\ \\ x = a$

Final answer:

Values of x and y are

$\boxed{x = a} \\ \\\boxed{ y = b}$

Hope it helps you.

Remark*: Question was corrected before answering.

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