Question

pair of liner equation in two variable x/a+y/b=a+b and x/a²+y/b²=2 (a+b is not equle to 0). so find the solution.
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Answer 1

Answer:

x = a², y = b²

Step-by-step explanation:

Given pair of linear equations

• x / a + y / b = a + b --- Eq( 1 )
• x / a² + x / b² = 2

Multiplying second equation with ' a '

⇒ a × ( x / a² + y / b² ) = 2 × a

⇒ x / a + ay / b² = 2a --- Eq( 2 )

Subtraction Eq( 1 ) from ( 2 )

⇒ x / a + ay / b² - ( x / a + y / b ) = 2a - ( a + b )

⇒ ay / b² - y / b = a - b

⇒ ( ay - yb ) / b² = a - b

⇒ [ y ( a - b ) ] / b² = a - b

⇒ y / b² = 1

⇒ y = b²

Substituting y = b² in Eq( 1 )

⇒ x / a + b² / b = a + b

⇒ x / a + b = a + b

⇒ x / a = a

⇒ x = a²

Therefore the value of x is a² and y is b².