6-1: Graphing Systems of Equations

Solve the inequality: -7x < -9x x < 2 2. x > 2 3. x < 7 4. x > 9

Solve the inequality: w > w > w > w > -12 / 5 4. w < 15

Solve |3a – 2| < a > 2 / 3 2. a < / 2 < a < / 3 < a < 2

Graph the solution set: -2 / 3 < a <

Write an inequality, and then solve the following: Ten less than five times a number is greater than ten. 1. 5n > 10; n > n – 10 > 10; n > n – 10 < 10; n < n < 10; n < 2

Lori had a quarter and some nickels in her pocket, but she had less than $0.80. What is the greatest number of nickels she could have had? nickels nickels nickels 4. 9 nickels

Which inequality does the graph below represent? 1. 3x – y < x + y > x – y > x + y < 1

6-1: Graphing Systems of Equations In Algebra 1A, you graphed linear equations Now  We will determine the number of solutions a system of linear equations has  Solve systems of linear equations by graphing

6-1: Graphing Systems of Equations New Vocabulary  System of Equations  A set of equations that all use the same variables  Consistent  A system of equations that has at least one ordered pair that satisfies both equations  Independent  A system of equations with exactly one solution  Dependent  A system of equations that has an infinite number of solutions  Inconsistent  A system of equations with no ordered pairs that satisfy both equations

6-1: Graphing Systems of Equations

Use the graph to determine whether the system is consistent or inconsistent and if it is independent or dependent TThe graphs are parallel, so there is no solution. The system is inconsistent.

Use the graph to determine whether the system is consistent or inconsistent and if it is independent or dependent TThe graphs intersect at exactly one point, so there is exactly one solution. The system is consistent and independent.

Use the graph to determine whether the system is consistent or inconsistent and if it is independent or dependent 1. Consistent and independent 2. Inconsistent 3. Consistent and dependent 4. Cannot be determined 2y + 3x = 6 y = x – 1

Use the graph to determine whether the system is consistent or inconsistent and if it is independent or dependent 1. Consistent and independent 2. Inconsistent 3. Consistent and dependent 4. Cannot be determined y = x + 4 y = x – 1

6-1: Graphing Systems of Equations Assignment  Page 338  Problems 1 – 6 and 10 – 15 (all)

6-1: Graphing Systems of Equations Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.  y = 2x + 3 8x – 4y = -12 The graphs coincide. There are infinitely many solutions of this system of equations.

6-1: Graphing Systems of Equations Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.  x – 2y = 4 x – 2y = -2 The graphs are parallel lines. Since they do not intersect, there are no solutions of this system of equations.

Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it. y = 2x + 3 y = ½ x One; (0, 3) 2. No solution 3. Infinitely many 4. One; (3, 3)

Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it. x + 3y = 4 1 / 3 x + y = One; (0, 0) 2. No solution 3. Infinitely many 4. One; (1, 3)

6-1: Graphing Systems of Equations Real World Example  Naresh rode 20 miles last week and plans to ride 35 miles per week. Diego rode 50 miles last week and plans to ride 25 miles per week. Predict the week in which Naresh and Diego will have ridden the same number of miles. Number of miles ridden EqualsNumber of miles per week TimesNumber of weeks since week one PlusMiles ridden in week one Let y = the total number of miles ridden Nareshy=35●x+20 Diegoy=25●x+50

6-1: Graphing Systems of Equations Graph the equations yy = 35x + 20 yy = 25x + 50 The graphs seem to intersect at the point (3, 125). You can check by substituting (3, 125) for (x, y) in each equation 1125 = 35(3) + 20 1125 = 25(3) + 50

Alex and Amber are both saving money for summer vacation. Alex has already saved $100 and plans to save $25 per week until the trip. Amber has $75 and plans to save $30 per week. In how many weeks will Alex and Amber have the same amount of money? weeks 2. 7 weeks 3. 5 weeks weeks

6-1: Graphing Systems of Equations Assignment  Page 338  Problems 7, 9, 17 – 25 (odds)