Systems of Equations and Systems of Equations and InequalitiesInequalities

Solving systems by Graphing

Solving systems by using Substitution

Solving systems using Elimination

Linear Inequalities

Why?

1. Find the x and y intercepts

When x = 0, y = -3

When y = 0, x = 9/4

2. Draw the line on your graph Is it a solid or dotted line? Why?

3. Will you shade above or below the line?

Systems of Linear Inequalities

Suppose you have a job in an ice cream shop that pays $6 per hour. You also have a babysitting job that pays $4 per hour. You want to earn at least $60 per week but you don’t want to work more than 12 hours per week.

a) Write a system of equations for this situation and graph the linear inequalities.

b) Give three possible solutions to the system.

Let x = # of hours at the ice cream shop & y = # hours babysitting.

Write an inequality for the hours worked per week x + y ≤ 12

Write an inequality for the money earned during the week. 6x + 4y ≥ 60

Draw the graph of this system of inequalities

Select three points in the shaded region.

1. The cost of three notebooks and four pencils is $8.50. The cost of five notebooks and eight pencils is $14.50. Determine the cost of one notebook and the cost of one pencil. [Only an algebraic solution can receive full credit.]

2. What is the solution set of the system of equations x + y = 5 and y = x2 – 25?

1) 2) 3) 4)

3. Which ordered pair is in the solution set of the system of inequalities shown in the graph below?

1) (-2,-1) 2) (-2,2) 3) (-2,-4) 4) (2,-2)

4. What is the solution of the system of equations shown in the graph below?

1) (1,0) and (-3,0) 2) (0,3) and (0,-1) 3) (-1,-2) 4) (-2,-1)