Solve for x and y : x/a =y/b , ax + by = a^2+ b^2
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Given
x/a=y/b
=>x/a-y/b=0
=>bx-ay=0 ----------(1)
or
ax+by=a^2+b^2----------(2)
Multiple a in equation (1)
Nd b in equation (2)
abx-a^2y=0
abx+b^2y=a^2b+b^3
(-) (-) (-) (-)
______________________
-y(a^2+b^2)= -b(a^2+b^2)
=> y=b [•-• because (-) (-) cancel Nd (a^2+b^2) also cancelled ]
Putting (y) value in equation (1)
bx-ay=0
=> bx-ab=0
=> b(x-a)=0
=>x-a=0/b=0
=>x-a=0
=> x=a
•°• The value of x=a, y=b
x/a=y/b
=>x/a-y/b=0
=>bx-ay=0 ----------(1)
or
ax+by=a^2+b^2----------(2)
Multiple a in equation (1)
Nd b in equation (2)
abx-a^2y=0
abx+b^2y=a^2b+b^3
(-) (-) (-) (-)
______________________
-y(a^2+b^2)= -b(a^2+b^2)
=> y=b [•-• because (-) (-) cancel Nd (a^2+b^2) also cancelled ]
Putting (y) value in equation (1)
bx-ay=0
=> bx-ab=0
=> b(x-a)=0
=>x-a=0/b=0
=>x-a=0
=> x=a
•°• The value of x=a, y=b
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