Find x and y values that make both y=-2/3x+3 and y=2x-5 true

x = 3, y = 1

Step-by-step explanation:

Given the 2 equations

y = - x + 3 → (1)

y = 2x - 5 → (2)

Substitute y = 2x - 5 into (1)

2x - 5 = - x + 3

Multiply through by 3 to clear the fraction

6x - 15 = - 2x + 9 ( add 2x to both sides )

8x - 15 = 9 ( add 15 to both sides )

8x = 24 ( divide both sides by 8 )

x = 3

Substitute x = 3 into either of the 2 equations and evaluate for y

Substituting into (2)

y = 2(3) - 5 = 6 - 5 = 1

Thus x = 3 and y = 1

v v cj van config k tbs eng r.c r.c fcb fb gb frfr

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