Unit 5 Lesson 1: Linear Systems: Solve by Graphing

Types of Solutions:1 Solution Infinite

SolutionsNo solution

Graph

Equations

y = mx + by = ax + c

y = mx + by = mx + b

y = mx + by = mx + c

In Terms of slope & y-intercept

Different slopes AND different y-intercepts OR Different slopes or same y-intercepts

Same slopes AND same y-intercepts

Same slopes AND different y-intercepts

Example #1: State the type of solution WITHOUT graphing.

1) { y=2 x+5y=−2 x+5

2) { y=3 x+2−3 x+ y=1

You Try…

{ y=2x+3−4 x+2 y=6

Example #2: Solve the system by graphing.

1) {x+2 y=−72x−3 y=0

You Try…

{2x+5 y=5−x+ y=2

Unit 5 Lesson 2: Linear Systems: Solve using Algebra

Solving by graphing by is only nice when the solution is “precise or exact.”

What happens when you have a situation like this?

We use Algebra!!!!

Example #1: Solve using Algebra by substitution.

1) {4 x+3 y=4x=7

2) {2 p+h=1006 p+h=200

You Try….

{2x−3 y=6x+ y=−12

Example #2: Solve by using Algebra by Elimination

1) {4 x−2 y=7x+2 y=3

2) {3 x+7 y=155x+2 y=−4

3) { 2x− y=3−2x+ y=−3

4) { 2x−3 y=18−2x+3 y=−6

You Try ………….

{3x−2 y=142 x+2 y=6

Unit 5 Lesson 3: Linear Systems Word Problems

If you have a word problem with 2 UNKNOWN values, you need to create 2 equations. Hence, a system.

Examples: Model each word problem as a system. Then solve.

1) An appliance store sells a washer and dryer for $1500. If the washer costs $200 more than the dryer, find the cost of each appliance.

2) A particular computer takes 43 nanoseconds to carry out five sums and seven products. It takes 36 nanoseconds to carry out four sums and six products. How long does it take the computer to carry out one sum? How long does it take the computer to carry out one product?

3) A bag contains pink marbles and green marbles, 49 in total. The number of pink marbles is 6 less than 4 times the number of green marbles. How many pink marbles are in the bag? How many green marbles are in the bag?

You Try….

Carol painted to types of shrubs. One shrub is 3 feet tall and grows 21 inches per year. The other shrub is 8 feet tall and grows 15 inches per year. When will the trees be the same height?

An animal shelter charges $2.50 per day to care for each cat and $4.50 per day to care for each dog. On Thursday, the shelter had 33 cats and dogs total. How many dogs were there on Thursday, if the total cost is $126.50?

Unit 5 Lesson 4: Graphing systems of Inequalities.Steps:1st – y-intercept use the slope to find the next point.2nd – Make a dotted line (<, >) or a solid line ( ≤ ,≥)3rd – Shade above the line (¿ , ≥) or below the line (¿ , ≤)If the line is vertical shade right (¿≥) or shade left (¿ , ≤)If the line is horizontal shade above the line (¿≥) or shade below the line (¿ , ≤)

Example #1: Solve and graph the inequality.

Example #2: Solve the system of linear inequalities. Don’t Forget to shade!!!

Unit 5 Lesson 5: ConstraintsExample #1: Find the x AND y values the will maximize or minimize the objective function.

Maximize for P = 2x + 3y Minimize for C = 7x + 4y Example #2: Graph each system of constraints. Name ALL the vertices. Identify the coordinate will maximize or minimize profit.

Vertices: Work: Coordinate:

Vertices: Work:

You Try….

Vertices: Work: