5y − x =10 , solve the equation for y?

5y-x=10

5y=10+x | : both sides

y=10/5+x/5

y=2+x/5

because

5y-x=5(2+x/5)-x=5x2+x/5x5-x=10+x-x=10

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4