How do I sort variable or solve for them?

Question

I have an equation: x/a + y/b = 1. I got the (wrong) answer of x/a + y = b. What did I do wrong and what do I have to do to get the right answer?

I am solving for the variable b.

Answer 1

First I would get rid of all the fractions. The common denominator is ab, so multiply everything by ab
(ab)(x/a) + (ab)(y/b) = (ab)(1)
Cancel a in the first term and b in the second term
bx + ay = ab
Bring all the terms with b to one side. You can do that by subtracting bx from each side
ay = ab - bx
Factor b on the right side
ay = b(a-x)
Divide both sides by (a-x)
ay/(a-x) = b

Answer 2

you probably need to solve for y:

multiply the whole thing by ba giving:

xb + ya = ab

then isolate ya:

ya = ab-xb

then divide by a:

y = b(a-x)/a

Answer 3

Solving for x

x/a + y/b = 1

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

bx + ay = ab

bx + ay - ay = ab - ay

bx = ab - ay

bx/b = ab - ay/b

x = a(b - y)/b

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Solving for y

x/a + y/b = 1

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

bx + ay = ab

bx + ay - bx = ab - bx

ay = ab - bx

ay/a = ab - bx/a

y = b(a - x)/a

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Solving fkor a

x/a + y/b = 1

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

bx + ay = ab

bx + ay - bx = ab - bx

ay = ab - bx

ay/y = ab - bx/y

a = b(a- x)/y

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solving for b

x/a + y/b = 1

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

bx + ay = ab

bx + ay - ay = ab - ay

bx = ab - ay

bx/x = ab - ay/x

b = a(b - x)/x