Respuesta :

sqdancefan

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Answer:

  a. 2x +y = 10; 2x +3y = 22

  b. 6 minutes

Step-by-step explanation:

a) The problem statement tells you that ...

  x = minutes around the block

  y = minutes around the park

  2x +y = 10 . . . . twice around the block and once around the park: 10 min

  2x +3y = 22 . . . twice around the block and 3 times around the park: 22 min

__

b) Subtracting the first equation from the second gives ...

  (2x +3y) -(2x +y) = (22) -(10)

  2y = 12 . . . . . . . . simplify

  y = 6 . . . . . . . . . divide by 2

It takes you 6 minutes to jog around the park.

spacedontknow

Answer:

Part A) The system of equations is

[tex]2x+y=10[/tex]

[tex]2x+3y=22[/tex]

Part B) The number of minutes it takes you to jog around the park is [tex]6[/tex] mins

Explanation:

Part A) Write a system of linear equations

Let [tex]x[/tex] ----> the number of minutes it takes you to jog around the block

Let [tex]y[/tex] ----> the number of minutes it takes you to jog around the park

we know that [tex]2x+y=10[/tex] ----> equation A

and [tex]2x+3y=22[/tex] ----> equation B

Part B) How long does it take you to jog around the park?

Multiply equation A by [tex]-1[/tex] both sides

[tex]-1(2x+y)=-10[/tex] ----> [tex]-2x-y=-10[/tex] ----> equation C

Adds equation B and equation C

[tex]2x+3y=22[/tex]

[tex]-2x-y=-10[/tex]

____________

[tex]3y-y=22-10[/tex]

[tex]2y=12[/tex]

[tex]y=6[/tex] minutes

Find the value of [tex]x[/tex]

[tex]2x+(6)=10[/tex]

[tex]2x=10-6[/tex]

[tex]x=4/2=2[/tex] minutes

Credit:

(This answer was originally made by calculista. All credit goes to them.)

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