Dylan works out and burns 10 calories per minute swimming and 7 calories per minute biking. he wants to burn a minimum of 600 calories. due to daylight limitations, the time dylan spends swimming must be no less than twice the time he spends biking. given that x is the number of minutes spent swimming and y is the number of minutes spent biking, determine which inequalities represent the constraints for this situation.

x is the number of minutes spent swimming  and burns 10 calories per minute swimming; it's 10x

y is the number of minutes spent biking and 7 calories per minute biking; it's 7y

He wants to burn a minimum of 600 calories; it's 10x + 7y <= 600

The time Dylan spends swimming must be no less than twice the time he spends biking; it's x >= 2y

So now you have the system of  inequalities:

10x + 7y <= 600

           x >= 2y

Substitute each points into the equations:

(44,25)

10(44)  + 7(25) <= 600

440 +175 <= 600

         615 > 600 >NO

44 >= 2(25)

44 < 50 >NO

(44,25) is NOT the solution of the system of equations

(46,20)

10(46)  + 7(20) <= 600

460 +140 <= 600

        600 <= 600 >YES

46 >= 2(20)

44 >=40 >YES

(46,20) is the solution of the system of equations

(37,19)

10(37)  + 7(19) <= 600

370 +133 <= 600

        503 <= 600 >YES

37 >= 2(19)

37 < 38 >NO

(37, 19) is NOT the solution of the system of equations

(52,12)

10(52)  + 7(12) <= 600

520 +84 <= 600

        604 > 600 >NO

52 >= 2(12)

52 >=24 >YES

(52, 12) is NOT the solution of the system of equations

Inequalities:

10x + 7y <= 600

           x >= 2y

Solution: (46,20)