3:1 Solving Systems of Equations by Graphing

To solve systems of equations by graphing To determine whether a system of linear

equations is consistent and independent, consistent and dependent or inconsistent

Warm-up: Type 1 writing3 lines or more – 2 minutes

In purchasing a cell phone, you could either pay $50/month + .02/text

or $40/month + .04/text.How do you know which plan to choose?

30 secondsFinish your thought.

System of equations: A set of two or more equations that contain the same variables

Example 1 Solve by GraphingExample 2 Break-Even Point AnalysisExample 3 Intersecting LinesExample 4 Same LineExample 5 Parallel Lines

Solve the system of equations by graphing.

Write each equation in slope-intercept form.

The graphs appear to intersect

at (4, 2).

Check Substitute the coordinates into each equation.

Answer: The solution of the system is (4, 2).

Original equations

Simplify.

Replace x with 4 and y with 2.

Solve the system of equations by graphing.

Answer: (4, 1)

Break-even point: In business applications, the point at which the income equals the cost

Fund-raising A service club is selling copies of their holiday cookbook to raise funds for a project. The printer’s set-up charge is $200, and each book costs $2 to print. The cookbooks will sell for $6 each. How many cookbooks must the members sell before they make a profit?

Let

Cost of books is cost per book plus set-up charge.

y = 2x + 200

Income from books is

price per book times

number of books.

y = 6 x

The graphs intersect at (50, 300). This is the break-even point. If the group sells less than 50 books, they will lose money. If the group sells more than 50 books, they will make a profit.

Answer:

The student government is selling candy bars. It cost $1 for each candy bar plus a $60 set-up fee. The group will sell the candy bars for $2.50 each. How many do they need to sell to break even?

Answer: 40 candy bars

Evaluate f(-4) for f(x) =│2x + 6│

1. 142. -23. 44. 125. 2

Name that function

1. Step2. Constant3. Absolute Value4. Round Down

Name that function

1. Step2. Constant3. Absolute Value4. Piecewise

Consistent:A system of equations that has at least one solutionInconsistent:A system of equations that has no solution (parallel lines)

Independent:A system of equations that has exactly one solution (intersecting lines)Dependent:A system of equations that has an infinite number of solutions (same line)

Graph the system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent.

Write each equation in slope-intercept form.

The graphs of the equations intersect at (2, –3). Since there is one solution to this system, this system is consistent and independent.

Answer:

Graph the system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent.

Answer:

consistent and independent

Graph the system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent.

Since the equations are equivalent, their graphs are the same line.

Any ordered pair representing a point on that line will satisfy both equations. So, there are infinitely many solutions. This system is consistent and dependent.

Answer:

Answer:consistent and dependent

Graph the system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent.

Graph the system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent.

The lines do not intersect. Their graphs are parallel lines. So, there are no solutions that satisfy both equations. This system is inconsistent.

Answer:

Graph the system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent.

Answer:

inconsistent