Use substitution to solve the following system of equation s 4y-3= 22 and y=2x-2

x = 33/8

y = 25/4

Step-by-step explanation:

4y - 3 = 22

y = 2x - 2

4y - 3 = 22

4y - 3 - 22 = 0

4y - 25 = 0

4(2x - 2) - 25 = 0

8x - 8 - 25 = 0

8x - 33 = 0

8x = 33

x = 33/8

y = 2x - 2

y = 2(33/8) - 2

y = 33/4 - 2

y = 33/4 - 8/4

y = 25/4

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