Warm-Up

The cost of bowling at bowling alley A or B is a function of the number of games g.

Cost A = 2.5g + 2Cost B = 2g + 4

When are the costs the same?

Solve Systems of Equations by

Graphing

CCGPS Coordinate Algebra

UNIT QUESTION: How do I justify and solve the solution to a system of equations or inequalities?Standard: MCC9-12.A.REI.1, 3, 5, 6, and 12

Learning Target:Students can find the solution to a system of equations by graphing.Standard: MCC9-12.A.REI.6

Given 2 lines in a coordinate plane, there can be 3 ways of

orientation…

The lines can intersect

The lines can be parallel

(same slope)

The lines can coincide (one on top of the

other)

Consistent vs. Inconsistent System

• A consistent system is a system that has at least one solution.

• An inconsistent system has no solution.

Dependent vs. Independent System

• An independent system has EXACTLY one solution.

• A dependent system has infinite solutions.

Classify the following as consistent, inconsistent,

dependent, or independent

Consistent Independent

Consistent Dependent

Inconsistent

Remember… There are 3 different types of systems of linear

equations

3 Different Systems:1) Consistent-independent2) Consistent-dependent3) Inconsistent

Steps1. Make sure each equation is

in slope-intercept form: y = mx + b.

2. Graph each equation on the same graph paper.

3. The point where the lines intersect is the solution. (If they don’t intersect then there’s no solution. If the lines are the same, there are infinite solutions)

4. Check your solution algebraically.

{𝒚=𝟑𝒙 −𝟏𝟐𝒚=−𝟐 𝒙+𝟑

1. Graph to find the solution.

Solution: (3, -3)

2. Graph to find the solution.

Solution: (-1, 3)

{2𝑥−2 𝑦=−82 𝑥+2 𝑦=4

No Solution

3. Graph to find the solution.

{𝑦=−2 𝑥+5𝑦=−2𝑥+1

Infinite Solutions

4. Graph to find the solution.

{ 2 𝑦=4 𝑥+6−8 𝑥+4 𝑦=12

Solution: (-2, 5)

5. Graph to find the solution.

{ 𝑦=5𝑥=−2

So basically…. If the lines have the same y-intercept b,

and the same slope m, then the system is consistent-dependent

If the lines have the same slope m, but different y-intercepts b, the system is inconsistent

If the lines have different slopes m, the system is consistent-independent

HWGuided Practice Questions 1-30. *Even #’s

Only*