Question

At tennis practice, Tim practices his backhand and his serve at least 2 hours each day. He works less on his backhand than his serve and practices his serve more than 1/2 hour daily.

Which system of inequalities represents Tim’s daily tennis practice if x represents the number of hours spent practicing his backhand and y represents the number of hours practicing his serve?
 

The images below are the possible answers,

Answer 1

He practices his backhand(x) and serve(y) AT LEAST(≥) 2 hours each day
x+y≥2

He practices his backhand(x) LESS THAN(<) his serves(y)
x<y

He practices his serves(y) MORE THAN(>) .5 hours
y>.5

Answer 2

`\left\{\begin{matrix}x+y\geq 2\\ x< y\\ y> (1)/(2)\end{matrix}\right.`

Explanation:

Let x represents the number of hours spent practicing his backhand

Let y represents the number of hours practicing his serve.

Since we are given that Tim practices his backhand and his serve at least 2 hours each day i.e. he practices his backhand and serves for two hours or more than two hours

⇒ x+y≥2 --(a)

We are also given that He works less on his backhand than his serve

⇒x < y --(b)

And we are also given that he practices his serve more than 1/2 hour daily.

⇒ y > 1/2 --(c)

Thus the inequalities are :

`\left\{\begin{matrix}x+y\geq 2\\ x< y\\ y> (1)/(2)\end{matrix}\right.`

Thus the Option C is correct .