Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.
There are two trails near Kirk's house that he runs regularly, a short loop and a long loop.
Last week, he ran 4 short loops and 6 long loops, for a total of 56 kilometers. This week, he
ran 1 long loop, covering a total of 8 kilometers. What is the length of each loop?
The short loop has a length of
kilometers.
kilometers, and the long loop has a length of

Answer is in the photo. I couldn't attach it here, but uploaded it to a file hosting. link below! Good Luck!

cutt.ly/XzW3SUN

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is