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You can jog around your block twice and the park once in 10 minutes. you can jog around your block twice and the park 3 times in 22 minutes.


a. write a system of linear equations that represents this situation. let x represent the number of minutes it takes you to jog around your block and y represent the number of minutes it takes you to jog around the park. system of equations:


b. how long does it take you to jog around the park? it takes you minutes to jog around the park.

Respuesta :

calculista

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\ min[/tex]

Step-by-step explanation:

Part a)  Write a system of linear equations

Let

x-----> the number of minutes it takes you to jog around your block

y---> the number of minutes it takes you to jog around the park

we know that

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

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

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

Multiply equation A by -1 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\\-2x-y=-10\\-------\\ 3y-y=22-10\\2y=12\\y=6\ minutes[/tex]

Find the value of x

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

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

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

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