1/3x+y=4 solve the equation for y.

y=4-x/3

Step-by-step explanation:

(1/3)x + y = 4

Subtract (1/3)x from both sides of the equation

 (1/3)x - (1/3)x + y = 4 - (1/3)x

 y = 4 - (1/3)x

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