Solving Systems of Equations Chapter 5

Solving Systems of Linear Equations by Graphing I can solve systems of linear equations by graphing.

Solving Systems of Linear Equations by Graphing Vocabulary (page 134 in Student Journal) system of linear equations: two or more linear equations with related variables solution of a system of linear equations: any ordered pair that makes all of the equations in the system true

Solving Systems of Linear Equations by Graphing Examples (space on page 134 in Student Journal) Determine if the ordered pair is a solution to the system of equations. (5, 1) b) (-1, -5) x + y = 6 y = -x + 2 2x – y = 9 y = 3x - 2

Solving Systems of Linear Equations by Graphing Solutions yes no

Solving Systems of Linear Equations by Graphing Solve the system by graphing. c)

Solving Systems of Linear Equations by Graphing Solution c) (2, 3)

Solving Systems of Linear Equations by Graphing Example d) Solve the system of equations by graphing. y = -2x + 5 y = 4x - 1

Solving Systems of Linear Equations by Graphing Solution d) (1, 3)

Solving Systems of Linear Equations by Graphing e) A museum sells 4 children’s tickets and 8 adult tickets for their morning show and makes $128. For the afternoon show, they make $72 by selling 6 adult tickets. What is the price of a children’s ticket?

Solving Systems of Linear Equations by Graphing Solution e) 4x + 8y = 128 6y = 72 x = 8 $8 per child’s ticket

Solving Systems of Linear Equations by Substitution I can solve systems of linear equations by substitution.

Solving Systems of Linear Equations by Substitution Core Concepts (page 139 in Student Journal) Steps for using Substitution Method 1. solve one equation for a variable 2. substitute the expression into the other equation for the variable and solve the new equation for the variable 3. substitute value of variable into either equation and solve for the other variable

Solving Systems of Linear Equations by Substitution Examples (space on page 139 in Student Journal) Solve the system by substitution. y = -x + 3 b) x – y = -4 3y + 5x = -1 2x + y = 4

Solving Systems of Linear Equations by Substitution Solutions (-5, 8) (0, 4)

Solving Systems of Linear Equations by Substitution c) An theater earns $3640 from a concert. An orchestra ticket costs 3 times as much as a balcony ticket. Below are the sales from a recent concert. What is the price of each type of ticket?

Solving Systems of Linear Equations by Substitution Solution c) y = 3x 148y + 76x = 3640 x = 21, y = 7 $21 orchestra ticket, $7 balcony ticket

Solving Systems of Linear Equations by Elimination I can solve systems of linear equations by elimination.

Solving Systems of Linear Equations by Elimination Core Concepts (page 144 in Student Journal) Steps for using Elimination Method if necessary, multiply one or both equations by a constant add or subtract to eliminate a variable 3. solve the resulting equations 4. substitute value of variable into either equation and solve for the other variable

Solving Systems of Linear Equations by Elimination Examples (space on page 144 in Student Journal) Solve the system by elimination. -2x + 3y = 4 b) 3x + 2y = -2 2x – y = -8 -6x – 5y = 2

Solving Systems of Linear Equations by Elimination Solutions (-5, -2) (-2, 2)

Solving Systems of Linear Equations by Elimination c) A shipping business has 2 locations. Location A has 3 large trucks and 2 small trucks, which cost $270,000. Location B has 4 large trucks and 3 small trucks, which cost $375,000. What is the cost of each type of truck?

Solving Systems of Linear Equations by Elimination Solution c) 3x + 2y = 270,000 4x + 3y = 375,000 (60000, 45000) $60,000 for the large truck and $45,000 for the small truck

Solving Special Systems of Linear Equations I can determine the numbers of solutions of linear systems.

Solving Special Systems of Linear Equations Core Concepts (page 149 in Student Journal) We will get 1 solution when the lines intersect. We will get no solutions when the lines are parallel. We get infinitely many solutions when the lines are the same.

Solving Special Systems of Linear Equations Examples (space on page 149 in Student Journal) Solve the system of linear equations. y = 3x + 2 b) x – 3y = 6 y = 3x – 1 3x – 9y = 18

Solving Special Systems of Linear Equations Solutions no solution infinitely many solutions

Graphing Linear Inequalities in Two Variables I can graph linear inequalities in 2 variables.

Graphing Linear Inequalities in Two Variables Vocabulary (page 159 in Student Journal) linear inequality in two variables: formed by replacing the equal sign in a linear equation with an inequality symbol solution of a linear inequality: an ordered pair that makes the inequality true

Graphing Linear Inequalities in Two Variables graph of a linear inequality: shows all of the solutions of the inequality in the coordinate plane half-plane: a region that is bounded by a line.

Graphing Linear Inequalities in Two Variables Core Concepts (page 159 in Student Journal) Guidelines for Graphing Linear Inequalities greater than/less than: use dashed line greater than or equal to/less than or equal to: use solid line greater than/greater than or equal to: shade above line less than/less than or equal to: shade below line

Graphing Linear Inequalities in Two Variables Examples (space on page 159 in Student Journal) Determine whether the ordered pair is a solution to the inequality. a) 3x – y < 2; (-2, 2) b) 4x – y > 5; (1, 3)

Graphing Linear Inequalities in Two Variables Solutions yes no

Graphing Linear Inequalities in Two Variables Graph in the coordinate plane. c) y ≥ -3 d) x + y < 2

Graphing Linear Inequalities in Two Variables Solutions c) d)

Graphing Linear Inequalities in Two Variables e) You can spend at most $9 for potatoes and carrots for a stew you are making. Potatoes are $3 a pound and carrots are $1.50 per pound. Write and graph an inequality that represents the amount of potatoes and carrots you can buy for the stew.

Graphing Linear Inequalities in Two Variables Solution e) 3x + 1.5y ≤ 9

Systems of Linear Inequalities I can graph systems of linear inequalities.

Systems of Linear Inequalities Vocabulary (page 164 in Student Journal) system of linear inequalities: made up of 2 or more linear inequalities solution to a system of linear inequalities: an ordered pair that makes all the inequalities in the system true

Systems of Linear Inequalities Examples (space on page 164 in Student Journal) Determine whether each ordered pair is a solution to the system of inequalities. y > 3x b) y > 3x y ≤ -x – 2 y ≤ -x – 2 (-2, -1) (0, 4)

Systems of Linear Inequalities Solutions yes no

Systems of Linear Inequalities Graph the system of inequalities. c) y ≥ -1 d) x – y > 2 y < -x + 2 x – y ≤ - 3

Systems of Linear Inequalities Solutions c) d) no solution

Systems of Linear Inequalities Write the system of inequalities from the graph. e) f)

Systems of Linear Inequalities Solutions e) y ≤ 2 y > -x + 1 f) x ≥ 1 y ≥ 1/2 x - 2

Systems of Linear Inequalities g) You have at most 7 hours to spend swimming and playing soccer. You want to spend at least 2 hours playing soccer and you want to spend more than 2 hours swimming. Write and graph a system to determine how much time you can spend on each activity.

Systems of Linear Inequalities Solution g) x + y ≤ 7 x ≥ 2 y > 2