To solve this problem using the system of equations:

We are given:

1. $x + y = 11$ (Kevin's hours + Jesse's hours = 11)
2. $y = 0.5x + 2$ (Jesse plays 2 more hours than half of Kevin's hours)

Let's solve this step by step:

Step 1: Substitute $y = 0.5x + 2$ into $x + y = 11$:

$x + (0.5x + 2) = 11$

Step 2: Simplify the equation:

$x + 0.5x + 2 = 11$ $1.5x + 2 = 11$

Step 3: Solve for $x$:

$1.5x = 11 - 2$ $1.5x = 9$ $x = \frac{9}{1.5}$ $x = 6$

Step 4: Substitute $x = 6$ into $y = 0.5x + 2$:

$y = 0.5(6) + 2$ $y = 3 + 2$ $y = 5$

Final Answer:

• Kevin ($x$) plays 6 hours.
• Jesse ($y$) plays 5 hours.

Thus, the correct response is D.

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Do you want more details or have any questions?

Related Questions:

1. How can we graphically represent this system of equations?
2. What if Jesse played 3 hours more instead of 2 hours more than half Kevin's hours?
3. How does solving by substitution compare to solving by elimination for this problem?
4. Could we solve this using matrices or determinants?
5. How can we check if the solution satisfies both equations?

Tip:

Always verify your solution by substituting it back into the original equations to ensure accuracy!