Solve each of the following systems of equations by the method of cross-multiplication:
x(a-b+ab/a-b)=y(a+b-ab/a-b)x+y=2a²
Answers
x = a( a² - b² - ab) /(a - b) , y = a( a² + b² - ab) /(a - b)
Step-by-step explanation:
x (a - b + ab/(a - b) = y (a + b - ab/a-b)
x + y = 2a²
x (a - b + ab/(a - b) = y (a + b - ab/a-b)
multiplying with a-b both sides
=> x( a² + b² - 2ab + ab) = y( a² - b² - ab)
=> x( a² + b² - ab) = y( a² - b² - ab)
x + y = 2a²
=> x + x ( a² + b² - ab)/( a² - b² - ab) = 2a²
=> x( 1 + ( a² + b² - ab)/( a² - b² - ab)) = 2a²
=> x( a² - b² - ab + a² + b² - ab)/( a² - b² - ab) = 2a²
=> x(2a² - 2ab) /( a² - b² - ab) = 2a²
=> x2a(a - b) /( a² - b² - ab) = 2a²
=> x(a - b)/( a² - b² - ab) = a
=> x = a( a² - b² - ab) /(a - b)
x + y = 2a²
=> y( (a² - b² - ab)/( a² + b² - ab) + y = 2a²
=> y((a² - b² - ab)/( a² + b² - ab) + 1) = 2a²
=> y(2a² - ab)/( a² + b² - ab) = 2a²
=> y(a - b) /( a² + b² - ab) = a
=> y = a( a² + b² - ab) /(a - b)
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