Question

solve the following system of equations by cross multiplication method

Answer 1

(x/a) + (y/b) = a + b

Multiply by (1/a) both sides, we get

(x/a²) + (y/ab) = 1 + (b/a)  ............ (1)

(x/a²) + (y/b²) = 2   .................. (2) (given)

Subtract (2) from (1), we get

(x/a²) + (y/ab)  - x/a² - y/b² = 1 + (b/a)

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

y/b² - y/ab = 1 - b/a

(yab - yb)/ab³ = 1 - b/a

(ya - yb)/ab² = 1 - b/a

y (a-b)/ab² = (a - b)/a

y = [b²(a-b)] / ( a-b)

y = b²

Now put  y = b² in equation x/a² + y/b² = 2

x/a² + b²/b² = 2

x/a² = 2- 1 = 1

x = a²

= bx + ay = (a+b)ab

= xb + ya = a²b + ab²

= a²b + ab² - xb - ya