Systems of Linear Equations; Substitution and Elimination

Slides:

Advertisements

Similar presentations

Warm-Up Tyler is catering a banquet for 250 people. Each person will be served either a chicken dish that costs $5 each or a beef dish that costs $7.

Advertisements

System of Linear Equations Project By Julian Rodriguez a.k.a Pablo.

A system of linear equations allows the relationship between two or more linear equations to be compared and analyzed. 5.1 – Systems of Linear Equations.

Using a 3 Variable System to find a Quadratic Equation.

7.4 Solving Polynomial Equations Objectives: Solve polynomial equations. Find the real zeros of polynomial functions and state the multiplicity of each.

Write a quadratic function in vertex form

7.1 SOLVING SYSTEMS BY GRAPHING The students will be able to: Identify solutions of linear equations in two variables. Solve systems of linear equations.

Algebra 1 Notes Lesson 7-2 Substitution. Mathematics Standards -Patterns, Functions and Algebra: Solve real- world problems that can be modeled using.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 11.1 Systems of Linear Equations; Substitution and Elimination.

3.4 “Solving Linear Systems with 3 Variables” The solutions are called an ordered triple (x,y,z). Equations are in the form of Ax + By + Cz = D. 1.4x +

3-D Systems Yay!. Review of Linear Systems Solve by substitution or elimination 1. x +2y = 11 2x + 3y = x + 4y = -1 2x + 5y = 4.

Objective: Solve a system of two linear equations in two variables by elimination. Standard: H. Select and use an appropriate strategy to solve.

Section 10.1 Systems of Linear Equations; Substitution and Elimination 1.

EXAMPLE 1 Write a quadratic function in vertex form Write a quadratic function for the parabola shown. SOLUTION Use vertex form because the vertex is given.

The Quadratic Formula. What does the Quadratic Formula Do ? The Quadratic formula allows you to find the roots of a quadratic equation (if they exist)

Solving Linear Inequalities `. Warm-up -4 < x ≤ 6 x ≤ -4 or x>

7.4 Solving Polynomial Equations Objectives: Solve polynomial equations. Find the real zeros of polynomial functions and state the multiplicity of each.

Algebra I Seminar Warm up word problems. Graphing a Line The average lifespan of American women has been tracked, and the model for the data is y = 2t.

Finding a Quadratic Equation from Three Coordinates.

1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 8-1 Quadratic Functions Chapter 8.

Section 4.7 – The Quadratic Formula Students will be able to: To solve equations using the Quadratic Formula To determine the number of solutions by using.

Section 5.3 Solving Systems of Equations Using the Elimination Method There are two methods to solve systems of equations: The Substitution Method The.

Objective: Solve a system of two linear equations in two variables by elimination. Standard: H. Select and use an appropriate strategy to solve.

BELL RINGER  Yesterday you learned 3 different ways to solve systems of linear equations. Do you have a preference on how to solve systems? Explain.

WORD PROBLEMS WITH SYSTEMS OF EQUATIONS Objective; Solve application problems using systems of equations.

Section 11.1 Systems of Linear Equations; Substitution and Elimination.

Systems of linear equations Problem—The school Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold.

Practice Word Problems Homework Answers Boat: 12 mph ; current: 9mph 7.Van: 8 ; Bus: 22 8.Van: 18 ; Bus: 59 9.senior citizen ticket: $4,

Standard form of a linear equation: Ax + By = C You can use the x and y intercepts to graph an equation. -Find the x intercept by substituting 0 for y.

Key Concepts for Sect. 7.1 *A system of equations is two or more equations in two or more variables. *Numerically, a solution to a system of equations.

Section 8.1 Systems of Linear Equations; Substitution and Elimination.

Do Now: Solve the system graphically.. Academy Algebra II/Trig 12.1: Systems of Linear Equations HW: p.847 (18, 22, 30, 34, 42, 46) Quiz 12.1, 12.7: Wed.

Section 7.1 Systems of Linear Equations in Two Variables.

Graphing Quadratic Equations SECTION 1.1. WHAT IS A QUADRATIC EQUATION? An equation of the form: y = ax 2 + bx + c (a, b, and c are constants) When graphed,

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.

5.8 – Solving Quadratic Inequalities Objectives: Write, solve, and graph a quadratic inequality in one variable. Write, solve, and graph a quadratic inequality.

1.11 Applications with systems I can… write and solve my own systems of linear equations.

Chapter 3 Section 2. EXAMPLE 1 Use the substitution method Solve the system using the substitution method. 2x + 5y = –5 x + 3y = 3 Equation 1 Equation.

Algebra II day 36 Chapter 3 Systems of Linear Equations.

Section 8.1 Systems of Linear Equations in Two Variables.

REVIEW OF 3-1 AND 3-2 A) Solve by graphing y = 2x – 1 y = -3/4x + 10

Solving Linear Systems

Write a quadratic function in vertex form

Do Now Use the standard form of a quadratic equation to find the a, b and c of each equation. ax2 + bx + c = 0 x2 – 6x + 10 = 0 2x2 + 3x + 4 = 0 x2 –

4.6 Quadratic formula.

X.2 Solving Systems of Linear Equations by Substitution

Algebra 1 Section 6.5 Graph linear inequalities in two variables.

7.3 Solving Equations Using Quadratic Techniques

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Solving Systems Using Elimination

Quadratic Inequalities

5.2 Properties of Parabolas

Solving Nonlinear Systems

Algebra I Section 9.3 Graph Quadratic Functions

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Systems of Linear Equations

Systems of Linear Equations; Substitution and Elimination

4.6 Quadratic formula.

Solve a system of linear equation in two variables

Use back - substitution to solve the triangular system. {image}

Systems of Linear Equations; Substitution and Elimination

Section 5.1 Systems of Linear Equations in Two Variables

The Quadratic Formula.

Warm-up: Find the equation of the parabola y = ax2 + bx + c that passes through the given points: (-1, 4), (1, -6), (2, -5) CW: 7.1 – 7.3 Systems Quiz.

Objective Solve quadratic equations by graphing.

Chapter 8 Quadratic Functions.

Systems of Equations Solve by Graphing.

Multivariable Linear Systems

Unit 1 – Section 9 “Applications of Systems of Equations”

Write Quadratic Functions and Models

Presentation transcript:

Systems of Linear Equations; Substitution and Elimination Section 12.1 Systems of Linear Equations; Substitution and Elimination

A movie theater sells tickets for $9 A movie theater sells tickets for $9.00 each, with seniors receiving a discount of $2.00. One evening the theater took in $4760 in revenue. If x represents the number of tickets sold at $9.00 and y the number of tickets sold at the discounted price of $7.00, write an equation that relates these variables. Suppose that we also know that 600 tickets were sold that evening. Can you write another equation relating the variable x and y?

OBJECTIVE 1

OBJECTIVE 2

A movie theater sells tickets for $9 A movie theater sells tickets for $9.00 each, with seniors receiving a discount of $2.00. One evening the theater sold 600 tickets and took in $4760 in revenue. How many of each type of ticket were sold?

OBJECTIVE 3

OBJECTIVE 4

OBJECTIVE 5

OBJECTIVE 6

OBJECTIVE 7

Find real numbers a, b, and c so that the graph of the quadratic function y = ax2 + bx+ c contains the points (– 2, 13), (0, 1) and (– 2, 3).