Question 1(Multiple Choice Worth 1 points) (04.06 LC)

Which of the following points lie in the solution set to the following system of inequalities?

y > −3x + 3
y > x + 2

A.(2, −5)
B.(−2, 5)
C.(2, 5)
D.(−2, −5)

C

Step-by-step explanation:

It’s convenient that there are only two x values you need to check, -2 and 2. Just insert it to see what y is appropriate.

x = -2: y > 6 + 3 = 9 (and y > -2 + 2 = 0 which is redundant here)

x = 2: y > 2 + 2 = 4 (and y > -6 + 3 = -3 which is redundant here)

So, neither B nor D is in the solution set with 5 < 9 and -5 < 9.

A isn’t in the solution set either with -5 < 4.

C is in the solution set with 5 > 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