Answer:
x = 3; y = 3/2; z = -1
Step-by-step explanation:
The diameter of the circle is 41, so the radius is 41/2.
DA, DB, and DC are radii of the circle, so their lengths are equal and they are half of the diameter.
DA = DB = DC = 41/2
Set each expression equal to 41/2.
Then you have a system of 3 equations in 3 variables.
8x + 2z - 3/2 = 41/2
6x + y + 1 = 41/2
11y - 2z + 2 = 41/2
Multiply both sides of all equations by 2 to get rid of the fractions.
16x + 4z - 3 = 41
12x + 2y + 2 = 41
22y - 4z + 4 = 41
Move all constants to the right side.
16x + 4z = 44 (I'll name this equation Equation 1.)
12x + 2y = 39 (This is Equation 2.)
22y - 4z = 37
Line up the variables.
16x + 4z = 44
12x + 2y = 39
22y - 4z = 37
We will use the elimination method.
Add the first and third equations to eliminate z.
Write the second equation below it.
16x + 22y = 81
12x + 2y = 39
Now you have a system of 2 equations in 2 unknowns.
We will now eliminate y. Multiply he second equation by -11 and write it below the first equation. Then add them.
16x + 22y = 81
(+) -132x - 22y = -429
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-116x = -348
Divide both sides by -116.
x = 3
Plug in 3 for x in Eq. 1 and solve for z.
16x + 4z = 44 Eq. 1
16(3) + 4z = 44
48 + 4z = 44
4z = -4
z = -1
Plug in 3 for x in Eq. 2 and solve for y.
12x + 2y = 39 Eq. 2
12(3) + 2y = 39
36 + 2y = 39
2y = 3
y = 3/2
Answer: x = 3; y = 3/2; z = -1
