3.3Systems of

Inequalities

Do Now• 1) Retrieve 2 different colored pencils and a ruler from the front.• 2) Here the answers to the homework from last night. For the “Do

Now”, please check your work. Check with a partner first if you have questions, and I will answer remaining questions.

1) 26 nickels2) $2.50/lb for cinnamon and $3.00/lb for spice3) $0.66 for the first three minutes and $0.19 for each additional4) 16 kg.5) 10 oz.6) rate in calm water=15/2 km/hr, rate of current=3/2 km/hr7) rate in calm water=16.5 mi/hr, rate of current=1.5 mi/hr8) 96/5 miles9) 10 kg. of the 5% solution and 30 kg. of the 25% solution

That’s I Can’t Believe It’s Not Butter!

Solving Systems of Inequalities

• Graph the inequalities separately (you may wish to use different colored pencils to do this). Remember when to use dotted lines and when to use solid lines!

• The solution is simply where the shaded regions overlap.

Example• Graph the system of inequalities:

Your Turn! • Graph the system of inequalities:

Write a System of Inequalities for the Solution

Region Below

Answer

Is it possible for a system of inequalities to have no solution?

Application• A person’s theoretical maximum heart rate is 220-x where x is

the person’s age in years (for ages 20-65 inclusive). When a person exercises, it is recommended that the person strive for a heart rate that is at least 70% of the maximum and at most 85% of the maximum.

Write and graph a system of linear inequalities to represent this situation, and use it to determine if a 40 year old with a heart rate of 150 bpm when exercising is within the target zone.

Solutionx=the person’s age and y=the person’s heart rate

We see that for a 40 year old, a heart rate of 150bpm is within the target zone of 126 to 153 bpm inclusive.

Give it a Try! • You want to make a health mix of nuts and raisins that

provides at least 1800 calories for a hike along the Appalachian Trail that has no more than 110 grams of fat and weighs no more than 20 ounces. Let n = nuts and r = raisins.

• Write and graph a system of inequalities to model this situation.

Solution• 150n + 90r ≥ 1800150 calories per oz. nuts, 90 for raisins• 13n ≤ 11013 grams of fat per oz. of nuts, max. fat 110 grams• n + r ≤ 20Number of ounces of nuts & raisins cannot exceed 20 oz.

One More Practice

Suppose a zoo keeper wants to fence a rectangular habitat for goats. The length of the habitat should be at least 80 ft and the distance around it should be no more than 310 ft. What are the possible dimensions of the habitat?