Solve the simultaneous equations y=x-2 and y=3x+5

(- 3.5, - 5.5 )

Step-by-step explanation:

Given the 2 equations

y = x - 2 → (1)

y = 3x + 5 → (2)

Substitute y = 3x + 5 into (1)

3x + 5 = x - 2 ( subtract x from both sides )

2x + 5 = - 2 ( subtract 5 from both sides )

2x = - 7 ( divide both sides by 2 )

x = - 3.5

Substitute x = - 3.5 into either of the 2 equations and evaluate for y

Substituting into (1)

y = - 3.5 - 2 = - 5.5

Solution is (- 3.5, - 5.5 )

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