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Option D

Step-by-step explanation:

If (1, 6) is the only solution of the system of equations and one of system of equations is,

y = 2x + 4

Then solution of the system will satisfy both the equations.

Option A

y = 4x - 7

By satisfying this equation by (1, 6),

6 = 4(1) - 7

6 = -3

False.

Therefore, given equation is not the answer.

Option B

y = 2x + 8

By satisfying this equation by (1, 6),

6 = 2(1) + 8

6 = 10

False.

Therefore, given equation is not the answer.

Option C

y = -2(x + 2)

By satisfying this equation by (1, 6),

6 = -2(1 + 2)

6 = -6

False.

Therefore, given equation is not the answer.

Option D

y = 5x + 1

By satisfying this equation by (1, 6),

6 = 5(1) + 1

6 = 6

True.

Therefore, this is one of the equations of the system of equations.

Option D is the answer.

answer: both chords and diameters have two endpoints on a circle. diameters must intersect the center of a circle.