SOLVING SYSTEMS OF LINEAR EQUATIONS IN TWO VARIABLES

SOLVING SYSTEMS OF LINEAR EQUATIONS IN TWO VARIABLES UNIT 1 DAY 10

KEY CONTENT: I can solve systems of linear equations exactly. I know the point of intersection of multiple graphs is the solution to the equations. I can find the intersection point of a function using various methods. I can solve a real-world problem by writing and

HOW CAN I SOLVE A LINEAR SYSTEM OF EQUATIONS? GRAPHING METHOD ELIMINATION METHOD (LINEAR COMINBATION) SUBSTIUTION METHOD CREATING A TABLE OF VALUES TECHNOLOGY

ELIMINATION METHOD: GOAL IS TO ADD EQUATIONS TO OBTAIN AN EQUATION IN ONE VARIABLE. Step 1: Line up equations by like columns Step 2: Multiply one or both of the equations by a constant to obtain coefficients that differ only in sign for one of the variables. Step 3: Add the revised equations from Step 1. Combining like terms will eliminate one of the variables. Solve for the remaining variable. Step 4: Substitute the value obtained in Step 2 into either of the original equations and solve for the other

Rearrange equations Substitute the value of y into one of the original equations. Multiply the 1 st equation by (2) so that the x-coefficients differ only in sign Add the revised equations together Solve for y Solve for x. Check your algebra using a graphing calculator.

GUIDED PRACTICE EXAMPLE 1

INDIVIDUAL PRACTICE EXAMPLE 2

GUIDED PRACTICE EXAMPLE 3

GUIDED PRACTICE EXAMPLE 3 Using a graphing calculator, how could you have used RREF (Reduced Row Echelon Form) to solve this problem?

NUMBER OF SOLUTIONS OF A LINEAR SYSTEM The relationship between the graph of a linear system and the system’s number of solutions is illustrated below.

LINEAR SYSTEMS WITH ONE SOLUTION One Solution Different Slopes Different y-intercepts Solution statement is an ordered pair Examples: (-1, 2) (3, -5) (7, 0)

LINEAR SYSTEMS WITH INFINITELY MANY SOLUTIONS Infinitely Many Solutions Same Slopes Same y-intercepts Solution statement is identical Examples: 0=0 -5=-5 7=7

LINEAR SYSTEMS WITH NO SOLUTION No Solution Same Slopes Different y-intercepts Solution statement makes No Sense (No Solution) Examples: 0=3 -5=5 10= 4

GUIDED PRACTICE EXAMPLE 4 HOW MANY SOLUTIONS DOES THE SYSTEM CONTAIN?

GUIDED PRACTICE EXAMPLE 4 No Solution

INDEPENDENT PRACTICE EXAMPLE 5 HOW MANY SOLUTIONS DOES THE SYSTEM CONTAIN?

INDEPENDENT PRACTICE EXAMPLE 5 Infinitely Many Solutions

Your family is planning a seven day trip to Florida. You estimate that it will cost $275 per day in Tampa and $400 per day in Orlando. Your total budget for seven days is $2300. How many days should you spend in each location?

Tampa, Florida Orlando, Florida $275 $400 7 days total/$2300 budget

Time (days) Budget (dollars)

Your family could spend three days in Orlando and four days in Tampa.

Your school is planning a 5 hour outing at the community park. The park rents bicycles for $8 per hour and rollerblades for $6 per hour. The total budget person is $34. How many hours should students

Bicycling Rollerblading $8 per hour $6 per hour 5 hours total/$34 budget per

Time (hours) Budget (dollars)

The school should have the students spend three hours bicycling and two hours

Selling Frozen Yogurt at a fair, you make $565 and use 250 cones. A single-scoop cone costs $2 and a double-scoop cone costs $2. 50. How many of each type of

Single-Scoop Double. Scoop $2 $2. 50 250 cones sold/$565 in sales

Total Cones Sold Total Sales

You sold 120 singlescoop cones and 130 double-scoop cones.

To connect a DVD player to a television, you need a cable with special connectors at both ends. Suppose you buy a 6 foot cable for $15. 50 and a 3 foot cable for $10. 25. Assuming that the cost of a cable is the sum of the cost of the two connectors and the cost of the cable itself, what would you expect to pay for a 4 foot cable? Explain your answer.

c = cost per foot of cable n = cost of one connector 6 ft cable cost $15. 50 3 ft cable cost $10. 25 Cost of cable is the sum of the cost of two connectors & the cable itself.

A four foot cable with connectors would cost $12.