1. Goal 4.03: Applications of Systems with Inequalities and Equations

2. *Remember the 3 Methods* SubstitutionGraphing y = 2xy = x + 2 4y + 2x = 14y = 2x Elimination 10x - 12y = 64 6x + 12y = 96

3. Relationship Examples The sum of two numbers is 59. Their difference is 11. What are the two numbers? Step 1: Identify the variables Step 2: Write the system of equations Step 3: Solve

4. Break Even Examples Rachel invested $400 in equipment to make t- shirts for her family reunion. Each t-shirt costs $4 to print and sells for $15. How many t-shirts must she sell before her small business breaks even?

5. Cost/Value Examples A restaurant charges $1.30 for 1 biscuit and 2 eggs. It charges $2.15 for 2 biscuits and 3 eggs. What is the cost of each biscuit and egg?

6. Examples Stephanie and Karen are saving money to purchase a stove for their mom. Stephanie has $140 and deposits $30 each day. Karen has $100 and deposits an additional $30 per day. After how many days will the sisters have the same amount of money saved?

7. Examples The length of a rectangle is 2 cm more than 4 times the width. If the perimeter of the rectangle is 84 cm, what are the dimensions?

8. Examples A group of 52 people attended a ball game. There were three times as many children as adults. Set up a system of equations that represents the numbers of adults and children who attended the game and solve the system to find the number of children who were in the group. A.a + c = 52 and a = c + 3; 39 adults and 25 children B.a + c = 52 and a = 3c; 39 adults and 13 children C.a + c = 52 and c = a + 3; 25 adults and 39 children D.a + c = 52 and c = 3a; 13 adults and 39 children

9. Examples Emily has a pet-care job that pays $5 per hour. She also does child care and charges $8 per hour. She wants to earn at least $125 each week but does not want to work more than 20 hours. Which situation would satisfy both requirements? A.Emily could do pet care for 12 hours and child care for 8 hours. B.Emily could do pet care for 14 hours and child care for 6 hours. C.Emily could do pet care for 8 hours and child care for 12 hours. D.Emily could do pet care for 10 hours and child care for 9 hours.