Question

B is the midpoint of line AC. AC = 100 . AB = x + y and BC = 3x-2y. Find x and y

Answer 1

if AC = 100, and B is the midpoint,
how long are AB and BC?

Answer 2

50

Answer 3

so AB = BC and each is 50

since AB = BC, and we know that AB = x + y, and that BC = 3x-2y

we can say that

x + y = 3x - 2y

# can you solve that for "x"? the answer will be in terms of "y"

Answer 4

I tried and i got 3y = 2x

Answer 5

yeap, and solving for "x" will be \(\bf 3y = 2x \implies \cfrac{3y}{2} = x\)

so now, we know that AB or BC are 50
so let's use say, BC = 3x-2y
3x - 2y = 50

but we also know that \(\bf x = \cfrac{3y}{2}\)
so let's replace "x" in 3x - 2y for that, since they're equal

\(\bf 3x - 2y = 50 \implies 3\left(\cfrac{3y}{2}\right) - 2y= 50 \implies \cfrac{9y}{2}-2y=50\\
\quad \\
\textit{multiplying both sides by 2, to get rid of the denominator}\\
2 \times\left(\cfrac{9y}{2}-2y\right)=2\times(50) \implies 9y -4y = 100\)


and if you solve for "y" there, you'll see what "y" is :)

Answer 6

so, once you get the value for "y"

you can use that, and plug in it on either equation, AB or BC and solve for "x" :)

Answer 7

thank you sm uch!