Solve x/a + y/b = a + b, x/a2 + y/b2 = 2

Problem : Solve x/a + y/b = a + b, x/a² + y/b² = 2

Doubt by Ananya

Solution :
 x/a + y/b = a + b
(bx+ay)/ab = a+b
bx + ay = ab(a+b) ---- (1)

x/a² + y/b² = 2
(b²x + a²y)/a²b² = 2
b²x + a²y = 2a²b²---- (2)

Solving these equations by elimination method

[ bx + ay = ab(a+b) ] × b
[ b²x + a²y = 2a²b² ] ×1

b²x + ab y = a²b² + ab³
b²x + a²y = 2a²b²
-      -          -
---------------------------------------------
0 + ay (b-a) = a²b² + ab³ - 2a²b²
----------------------------------------------

ay (b-a) = ab² - a²b²
ay (b-a) = ab² (b-a)
ay = ab²
y = b²

putting this value of y in equation (1)

bx + a(b²) = ab(a+b)
bx = a²b + ab² -ab²
bx = a²b
x = a² 
Pro Tip - Try to solve these questions by cross multiplication method.