Solving Systems by Substitution

Slides:

Advertisements

Similar presentations

Equations and Their Solutions

Advertisements

Systems of Linear Equations Vocabulary. This is a System of Linear Equations.

Vocabulary Chapter 6.

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.

EOC Practice #18 SPI EOC Practice #18 Solve systems of linear equations/inequalities in two variables.

Thinking Mathematically Algebra: Graphs, Functions and Linear Systems 7.3 Systems of Linear Equations In Two Variables.

Solving Systems by Graphing

4.4 Equations as Relations

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.

Even though he knows you are slightly cracked.” "A true friend is someone who thinks you are a good egg.

Systems of Linear Equations in Two Variables. 1. Determine whether the given ordered pair is a solution of the system.

Warm-up 4-1. x – y = 33x + y = 52y = 6 – x x + y = 5x – 2y = 43x – 2y = 6 Graphs:

Solving Systems by Substitution

Solving Linear Systems by Substitution

WARM UP GRAPHING LINES Write the equation in slope- intercept form and then Graph. (Lesson 4.7) 1.3x + y = 1 2.x + y = 0 3.y = -4 3.

SYSTEMS OF EQUATIONS. SYSTEM OF EQUATIONS -Two or more linear equations involving the same variable.

6-2 SOLVING LINEAR SYSTEMS BY SUBSTITUTION Goal: Use substitution to solve a linear system Eligible Content: A / A

3.1 Solving Systems By Graphing Or Substitution. * A system of equations is a collection of equations in the same variable. *A solution to a system is.

5.1 Solving Systems of Equations Objectives: --To identify a system of equations --To determine if a point is a solution to a system --To use graphing.

Lesson 9.6 Topic/ Objective: To solve non linear systems of equations. EQ: How do you find the point of intersection between two equations when one is.

3.5 Solving systems of equations in three variables Main Ideas Solve systems of linear equations in three variables. Solve real-world problems using systems.

Solving Systems by Elimination

Solving Linear Systems by Substitution

Lesson 4-1 Solving linear system of equations by graphing

Algebra 1 Review Systems of Linear Equations Using Substitution

Solving Systems of Equations using Substitution

6-1 Linear Systems Goal: Solve a system of linear equations by graphing Eligible Content: A / A

Warm Up: Graph y = - 2x + 7 and find the x-intercept and y-intercept.

Core Focus on Linear Equations

Warm Up Evaluate each expression for x = 1 and y =–3.

Warm Up Evaluate each expression for x = 1 and y =–3.

6-2 Solving Systems using Substitution

Solving Systems Using Elimination

Warm Up 3x + 5y = 25 4x + 7y = 34 Find the value of x and y so that both equations are true.

Solve a system of linear equation in two variables

Lesson 15 Linear Equations The Slope Formula.

Lesson 7-4 part 3 Solving Systems by Elimination

Lesson 7-4 part 2 Solving Systems by Elimination

Lesson 4 Lines & Angles Vertical Angles.

Writing Linear Equations From Key Information

Before: November 28, 2017 Solve each system by graphing. 1. y = 2x – 1

Simplifying Algebraic Expressions

Solving One-Step Equations

Systems of Linear Equations in Two Variables

9.3 – Graphing Linear Equations

Warm Up Evaluate each expression for x = 1 and y =–3.

Rational Numbers & Equations

Systems of equations.

Lesson 7-4 part 3 Solving Systems by Elimination

Expressions and Equations

Before: December 4, 2017 Solve each system by substitution. Steps:

Warm Up Solve each quadratic equation by factoring. Check your answer.

6-1 Linear Systems Goal: Solve a system of linear equations by graphing Eligible Content: A / A

Lesson Objectives: I will be able to …

Warm Up Evaluate each expression for x = 1 and y =–3.

6-2 Solving Linear Systems by substitution

If you can easily isolate one of the variables,

Tie to LO Activating Prior Knowledge – 1. y – x = x + 3y = 6

Objectives Identify solutions of linear equations in two variables.

Choosing the Best Method

Systems of Equations.

Systems of Equations Solve by Graphing.

Tie to LO Activating Prior Knowledge – 1. y – 2x = x + 3y = 6

6.2 Using Substitution to Solve Systems

1-2 Solving Linear Systems

Chapter 9 Lesson 4 Solve Linear Systems By Substitution

Use Graphs of Functions

Warm- Up: Solve by Substitution

Solving Linear Systems by Graphing

Presentation transcript:

Solving Systems by Substitution Lesson 25 Linear Equations Solving Systems by Substitution

Warm-Up Solve each equation for x. 3x + 4x – 7 = 21 10 + 2x – 4x = 12

Solving Systems by Substitution Target: Determine the solution to a system of equations using the substitution method.

Vocabulary Substitution Method: A method for solving a system of equations.

Solving Systems of Linear Equations by Substitution Solve one of the linear equations for a variable (isolate x or y), if necessary. Replace the variable in the second equation with the expression that you solved for in Step 1. Solve for the variable in your new equation. Substitute your solution into the equation from Step 1 to find the value of the other variable. State your full answer as an ordered pair (x, y). Verify that the ordered pair is the solution by substituting the x- and y-values into both equations in the system or by graphing the system to confirm that the point of intersection matches your solution.

Example 1 y = –2(3) + 5 y = –6 + 5 y = –1 Solution: (3, –1) Use the substitution method to solve the system of linear equations. y = –2x + 5 4x + 3y = 9 4x + 3(–2x + 5) = 9 4x – 6x + 15 = 9 –2x + 15 = 9 – 15 – 15 –2x = –6 –2 –2 x = 3 y = –2(3) + 5 y = –6 + 5 y = –1 Solution: (3, –1)

Exit Problems Solve the system of equations using the substitution method. x = 4y – 5 2x + 3y = 23

Communication Prompt Why do you think there are multiple methods in mathematics to find the answer to a problem?