1. Solving Systems of Equations and Inequalities continued…
EQ: How do I solve real-world systems of equations and inequalities involving word problems?

2. Solving Real-World “Word” Problems involving systems of equations/inequalities
Any word problem can be solved using these following steps:
STEP 1: highlight the important information in the problem
STEP 2: identify your variables;
STEP 3: Write/create your first equation or inequality based on the information given
STEP 4: Write/create your second equation or inequality
STEP 5: Graphing both equations/inequalities
STEP 6: Solve/Identify your solution
Equations will be solved by finding the point(s) of intersections
Inequalities will be solved by finding where the two shaded areas meet

3. EXAMPLE: Solving Real-World Systems of Equations
Two rental car companies are running specials this month. At Orlando's Rentals, customers will pay $50 to rent a mid-sized car for the first day, plus $2 for each additional day. At Somerville Rent-a-Car, the price for a mid-sized car is $30 for the first day and $4 for every additional day beyond that. At some point, renting from either one of the companies would cost a customer the same amount. How many additional days would that take?

4. STEP 1: highlight the important information in the problem
Two rental car companies are running specials this month. At Orlando's Rentals, customers will pay $50 to rent a mid-sized car for the first day, plus $2 for each additional day. At Somerville Rent-a-Car, the price for a mid-sized car is $30 for the first day and $4 for every additional day beyond that. At some point, renting from either one of the companies would cost a customer the same amount. How many additional days would that take?

5. Somerville’s Rentals: y = 4x +30
STEP 2: identify your variables
Let x = each additional day
Let y = the total cost in dollars for the rental
STEP 3: Write/create your first equation or inequality based on the information given
Orlando’s Rentals: y = 2x + 50
STEP 4: Write/create your second equation or inequality
Somerville’s Rentals: y = 4x +30

6. STEP 5: Graphing both equations/inequalities
STEP 6: Solve/Identify your solution The intersection is at the point (10,70) This means that both rental companies will charge the same amount after 10 additional days, and that would cost $70

7. EXAMPLE: Solving Real-World Systems of Inequalities

10. Finally, graph each inequality (don’t forget to include a dashed or solid line where necessary) and shade!