Two lines, A and B, are represented by the following equations: Line A: y = x − 1
Line B: y = −3x + 11

Which of the following options shows the solution to the system of equations and explains why? (4 points)

a
(3, 2), because the point does not lie on any axis

b
(3, 2), because one of the lines passes through this point

c
(3, 2), because the point lies between the two axes

d
(3, 2), because both lines pass through this point

The solution to the system of equations is (3, 2) and because both lines pass through this point.

Hence, option D is correct.

Step-by-step explanation:

Given the system of equations

Line A: y = x − 1

Line B: y = −3x + 11

Arrange equation variables for elimination

subtracting the equations

solving 4x = 12 for x

divide both sides by 4

Simplify

For y = x − 1, substutute x = 3

y = x-1

y = 3 - 1

y = 2

Thus,

(x, y) = (3, 2)

Therefore,

The solution to the system of equations is (3, 2) and because both lines pass through this point.

Hence, option D is correct.

answer: the distance

step-by-step explanation:

to calculate the distance d of a line segment with endpoints (x1, y1) and (x2, y2) use the formula d (x2 x1)2 (y2 y1)2. to calculate the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) use the formula