Do Now 12/11/18 Take out HW from last night.

Slides:



Advertisements
Similar presentations
Do Now 1/10/11 Copy HW in your planner. Copy HW in your planner. Text p. 430, #4-20 evens, evens Text p. 430, #4-20 evens, evens Text p. 439,
Advertisements

6-1 Solving Systems by Graphing Warm Up Evaluate each expression for x = 1 and y = –3. 1. x – 4y 2. –2x + y Write each expression in slope- intercept form.
5-1 Solving Systems by Graphing
Solve Linear Systems by Substitution
7 = 7 SOLUTION EXAMPLE 1 Check the intersection point Use the graph to solve the system. Then check your solution algebraically. x + 2y = 7 Equation 1.
Chapter 5: Systems of Linear Equations Section 5.1: Solving Systems of Linear Equations by Graphing.
Chapter 7.1 Notes: Solve Linear Systems by Graphing Goal: You will solve a system of linear equations graphically.
Do Now 1/12/12  In your notebook, answer the following question. During a football game, a bag of popcorn sells for $2.50 and a pretzel sells for $2.00.
Substitute 0 for y. Write original equation. To find the x- intercept, substitute 0 for y and solve for x. SOLUTION Find the x- intercept and the y- intercept.
Substitute 0 for y. Write original equation. To find the x- intercept, substitute 0 for y and solve for x. SOLUTION Find the x- intercept and the y- intercept.
Chapter 7.2 Notes: Solve Linear Systems by Substitution
Warm Up Evaluate each expression for x = 1 and y =–3.
HOMEWORK FOR 7-1 p , 6, 8, 9, 14, 17, 18, 25, 32, 34, 42, 46 “Finish the whole thing; it’ll make my mom happy!” Colby.
Warm Up Evaluate each expression for x = 1 and y =–3. 1. x – 4y 2. –2x + y Write each expression in slope-intercept form, then then graph. 3. y – x = 1.
EXAMPLE 4 Solve a multi-step problem A business rents in-line skates and bicycles. During one day, the business has a total of 25 rentals and collects.
Objective: To solve systems of equations by graphing.
Warm-up 4-1. x – y = 33x + y = 52y = 6 – x x + y = 5x – 2y = 43x – 2y = 6 Graphs:
Section 3.4 Solving Systems of Linear Equations in Two Variables by the Substitution Method.
7.2 Solving Linear Systems by Substitution. Steps: 1. Solve one of the equations for one of the variables. 2.Substitute that expression into the other.
Table of Contents Topic Page # A Absolute Value Less ThAND B Absolute Value GreatOR Than Two Variable Inequalities Solve Systems.
What does a “solution” look like? So, what’s the solution here?
EXAMPLE 1 Solve a system graphically Graph the linear system and estimate the solution. Then check the solution algebraically. 4x + y = 8 2x – 3y = 18.
5.1 Solving Systems of Linear Equations by Graphing
7.1 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Solve Linear Systems by Graphing.
Solving Systems by Graphing
Lesson 4-1 Solving linear system of equations by graphing
X.2 Solving Systems of Linear Equations by Substitution
6-1 Linear Systems Goal: Solve a system of linear equations by graphing Eligible Content: A / A
Solving Systems by Graphing
System of Equations Substitution Method Day 1
1. Graph the equation –2x + y = 1.
Warm Up Evaluate each expression for x = 1 and y =–3.
Solving Systems by Graphing
Solving Systems by Graphing
Warm Up Evaluate each expression for x = 1 and y =–3.
Solving Systems by Graphing
Solving Systems by Graphing
Warm Up Evaluate each expression for x = 1 and y =–3.
Solve a system of linear equation in two variables
Lesson 7-4 part 2 Solving Systems by Elimination
Solving Systems by Graphing
Warm Up Evaluate each expression for x = 1 and y =–3.
Methods to Solving Systems of Equations
MS Algebra A-F-IF-7 – Ch. 7.1 Solve Linear Systems by Graphing
Warm Up Evaluate each expression for x = 1 and y =–3.
Solving Systems by Graphing
Section 7.1 “Solve Linear Systems by Graphing”
Before: December 4, 2017 Solve each system by substitution. Steps:
Solving Systems by Graphing
Solving Systems by Graphing
6-1 Linear Systems Goal: Solve a system of linear equations by graphing Eligible Content: A / A
Lesson Objectives: I will be able to …
Solving Systems by Graphing
Warm Up Evaluate each expression for x = 1 and y =–3.
Solving Systems by Graphing
Solve Linear Systems by Substitution
Skill Check over Solving Systems by Graphing after Homework Check
If you can easily isolate one of the variables,
Solving Systems by Graphing
Solving Systems by Graphing
Objectives Identify solutions of linear equations in two variables.
Solving Systems by Graphing
All solutions of a linear equation are on its graph
Solving Systems by Graphing
Solving Systems by Graphing
Solving Systems by Graphing
Solving Systems by Graphing
Solving Systems by Graphing
Solving Systems by Graphing
Do Now 12/14/18 y = 2x + 5 3x + y = 10 9x + 2y = 39 6x + 13y = -9
Presentation transcript:

Do Now 12/11/18 Take out HW from last night. Text p. 239, #4-22 evens, 27 & 28 Copy HW in your planner. Text p. 245, #9-18 all, 20 & 27 GoFormative.com. Solve the system below by graphing. x – y = 4 4x + y = 1

Solve the system by graphing. x – y = 4 4x + y = 1 Section 3.4

Homework Text p. 239, #4-22 evens, 27 & 28

Learning Goal Learning Target Students will be able to write and graph systems of linear equations. Learning Target Students will be able to solve systems of linear equations by substitution

Section 5.1 “Solve Linear Systems by Graphing” consists of two more linear equations. x + 2y = 7 Equation 1 3x – 2y = 5 Equation 2 A solution to a linear system is an ordered pair (a point) where the two linear equations (lines) intersect (cross).

Solve a multi-step problem A business rents in-line skates and bicycles. During one day, the business has a total of 25 rentals and collects $450 for the rentals. Find the number of pairs of skates rented and the number of bicycles rented. STEP 1 Write a linear system. Let x be the number of pairs of skates rented, and let y be the number of bicycles rented. x + y =25 Equation for number of rentals 15x + 30y = 450 Equation for money collected from rentals

Solve a multi-step problem Graph both equations. STEP 3 Estimate the point of intersection. The two lines appear to intersect at (20, 5). STEP 4 Check whether (20, 5) is a solution. 20 + 5 25 = ? 15(20) + 30(5) 450 = ? 25 = 25 450 = 450 ANSWER The business rented 20 pairs of skates and 5 bicycles.

Section 5.2 “Solve Linear Systems by Substitution” Solving a Linear System by Substitution Solve one of the equations for one of its variables. (When possible, solve for a variable that has a coefficient of 1 or -1). (2) Substitute the expression from step 1 into the other equation and solve for the other variable. (3) Substitute the value from step 2 into the revised equation from step 1 and solve.

“Solve Linear Systems by Substituting” y = 3x + 2 Equation 1 x + 2y = 11 Equation 2 x + 2(3x + 2) = 11 x + 2y = 11 Substitute x + 6x + 4 = 11 7x + 4 = 11 x = 1 y = 3x + 2 Equation 1 Substitute value for x into the original equation y = 3(1) + 2 y = 5 (5) = 3(1) + 2 5 = 5 The solution is the point (1,5). Substitute (1,5) into both equations to check. (1) + 2(5) = 11 11 = 11

“Solve Linear Systems by Substituting” Equation 1 x – 2y = -6 x = -6 + 2y Equation 2 4x + 6y = 4 4x + 6y = 4 4(-6 + 2y) + 6y = 4 Substitute -24 + 8y + 6y = 4 -24 + 14y = 4 y = 2 x – 2y = -6 Equation 1 Substitute value for x into the original equation x = -6 + 2(2) x = -2 (-2) - 2(2) = -6 -6 = -6 The solution is the point (-2,2). Substitute (-2,2) into both equations to check. 4(-2) + 6(2) = 4 4 = 4

Solve a multi-step problem A business rents in-line skates and bicycles. During one day, the business has a total of 25 rentals and collects $450 for the rentals. Find the number of pairs of skates rented and the number of bicycles rented. STEP 1 Write a linear system. Let x be the number of pairs of skates rented, and let y be the number of bicycles rented. x + y =25 Equation for number of rentals 15x + 30y = 450 Equation for money collected from rentals

Solve a multi-step problem Solve equation 1 for x. Equation 1 x + y = 25 x = 25 - y Equation 2 15x + 30y = 450 Substitute 15(25 - y) + 30y = 450 15x + 30y = 450 375 - 15y + 30y = 450 375 + 15y = 450 15y = 75 y = 5 x + y = 25 Equation 1 Substitute value for x into the original equation x + (5) = 25 ANSWER The business rented 20 pairs of skates and 5 bicycles. x = 20

During a football game, a bag of popcorn sells for $2 During a football game, a bag of popcorn sells for $2.50 and a pretzel sells for $2.00. The total amount of money collected during the game was $336. Twice as many bags of popcorn sold compared to pretzels. How many bags of popcorn and pretzels were sold during the game? $2.00x + $2.50y = $336 x = y = 2x y = 96 bags of popcorn and 48 pretzels

Guided Practice y = 2x + 5 3x + y = 10 x – y = 3 x + 2y = -6 (1, 7) (0, -3)

Homework Text p. 245, #9-18 all, 20 & 27