Drag each set of column entries to the correct location in the matrix equation. not all sets of entries will be used. a biker needs to pass two checkpoints before completing a race. the total distance for the race is 120 miles. the distance from the starting point to checkpoint 1 is 35 miles more than half the distance from checkpoint 1 to checkpoint 2. the distance from checkpoint 2 to the finish line is 20 miles less than twice the distance from checkpoint 1 to checkpoint 2. let x represent the distance from the starting point to checkpoint 1, y represent the distance from checkpoint 1 to checkpoint 2, and z represent the distance from checkpoint 2 to the finish line. complete the matrix equation that models this situation, a-1b = x.

The matrix equation is

Step-by-step explanation:

* Lets change the story problem to equations

- The distance between the starting point and checkpoint 1 is x

- The distance between checkpoint 1 to checkpoint 2 is y

- The distance between checkpoint and the finish line is z

- The total distance for the race is 120 miles

∴ x + y + z = 120 ⇒ (1)

-The distance from the starting point to checkpoint 1 is 35 miles

 more than half the distance from checkpoint 1 to checkpoint 2

∵ The distance from the starting point to checkpoint 1 is x

∵ The distance from checkpoint 1 to checkpoint 2 is y

- x is more than half y by 35

∴ x = 35 + (1/2) y ⇒ subtract (1/2) y from both sides

∴ x - (1/2) y = 35 ⇒ (2)

- The distance from checkpoint 2 to the finish line is 20 miles less

 than twice the distance from checkpoint 1 to checkpoint 2

∵ The distance from checkpoint 2 to the finish line is z

∵ the distance from checkpoint 1 to checkpoint 2 is y

- z is less than twice y by 20

∴ z = 2y - 20 ⇒ add 20 to both sides

∴ z + 20 = 2y ⇒ subtract z from both sides

∴ 2y - z = 20 ⇒ (3)

* Now lets write the three equations

# x + y + z = 120 ⇒ (1)

# x - (1/2) y = 35 ⇒ (2)

# 2y - z = 20 ⇒ (3)

- Now lets write the matrix equation that models this situation

∴

x/3-10=8

x/3=18

x=48

answer: entity is prob the answer

step-by-step explanation: