Solving Systems of Linear Equations in Two Variables: When you have two equations, each with x and y, and you figure out one value for x and one value.

Slides:

Advertisements

Similar presentations

Directions: Solve the linear systems of equations by graphing. Use the graph paper from the table. Tell whether you think the problems have one solution,

Advertisements

Adapted from Walch Education Proving Equivalencies.

Solving a System of Equations by ELIMINATION. Elimination Solving systems by Elimination: 1.Line up like terms in standard form x + y = # (you may have.

5.1 Solving Systems of Linear Equations by Graphing

Solving Systems of Linear Equations

Solving Linear Equations

Unit 1.3 USE YOUR CALCULATOR!!!.

8.1 Solving Systems of Linear Equations by Graphing

System of equations and Inequalities….! By Cory Hunter.

Solving Linear Systems by Elimination Math Tech II Everette Keller.

Solving Systems of Linear Equations in Two Variables

Goal: Solve a system of linear equations in two variables by the linear combination method.

Lesson 4-2: Solving Systems – Substitution & Linear Combinations

Solving a System of Equations in Two Variables By Elimination Chapter 8.3.

Solving Systems Using Elimination

SOLVING SYSTEMS ALGEBRAICALLY SECTION 3-2. SOLVING BY SUBSTITUTION 1) 3x + 4y = 12 STEP 1 : SOLVE ONE EQUATION FOR ONE OF THE VARIABLES 2) 2x + y = 10.

SYSTEMS OF LINEAR EQUATIONS SUBSTITUTION AND ELIMINATION Objectives: Solve Systems of Equations by Substitution and Elimination Identify Inconsistent Systems.

What is a System of Linear Equations? A system of linear equations is simply two or more linear equations using the same variables. We will only be dealing.

2010.  A first degree equation is called a linear equation in two variables if it contains two distinct variables.

Systems of Equations: Substitution Method

3-2 Solving Linear Systems Algebraically Objective: CA 2.0: Students solve system of linear equations in two variables algebraically.

Do Now (3x + y) – (2x + y) 4(2x + 3y) – (8x – y)

Lesson 2.8 Solving Systems of Equations by Elimination 1.

Chapter 4 Section 4.1 Solving Systems of Equations in Two Variables.

Ch : Solving Systems of Equations Algebraically.

6.2 Solve a System by Using Linear Combinations

Bell Ringer: Combine like terms 1)4x + (-7x) = 2)-6y + 6y = 3)-5 – (-5) = 4)8 – (-8) =

SOLVING SYSTEMS USING ELIMINATION 6-3. Solve the linear system using elimination. 5x – 6y = -32 3x + 6y = 48 (2, 7)

3.2 Solving Systems Algebraically When you try to solve a system of equations by graphing, the coordinates of the point of intersection may not be obvious.

Multiply one equation, then add

Solving Systems by Elimination 5.4 NOTES, DATE ____________.

Chapter 5: Systems of Linear Equations Section 5.1: Solving Systems of Linear Equations by Elimination.

Solving Systems of Linear Equations in 2 Variables Section 4.1.

SECTION 3.2 SOLVING LINEAR SYSTEMS ALGEBRAICALLY Advanced Algebra Notes.

WARM-UP. SYSTEMS OF EQUATIONS: ELIMINATION 1)Rewrite each equation in standard form, eliminating fraction coefficients. 2)If necessary, multiply one.

Solving Systems of Equation Using Elimination. Another method for solving systems of equations Eliminate one of the variables by adding the two equations.

Solving a System of Equations by ELIMINATION. Elimination Solving systems by Elimination: 1.Line up like terms in standard form x + y = # (you may have.

objective I Can state the first step for solving systems. I Can solve systems of equations by graphing, substitution or elimination.

Systems of Equations Draw 2 lines on a piece of paper. There are three possible outcomes.

Solve Linear Systems By Multiplying First

6) x + 2y = 2 x – 4y = 14.

Solve by Graphing Solve: 3x + 4y = - 4 x + 2y = 2

3.5: Solving Nonlinear Systems

Example: Solve the equation. Multiply both sides by 5. Simplify both sides. Add –3y to both sides. Simplify both sides. Add –30 to both sides. Simplify.

Solving Systems of Linear Equations in 3 Variables.

Solving Linear Equations

Warm Up Simplify each expression. 1. 3x + 2y – 5x – 2y

Break even or intersection

REVIEW: Solving Linear Systems by Elimination

Lesson 7.1 How do you solve systems of linear equations by graphing?

Methods to Solving Systems of Equations

Objectives Solve systems of linear equations in two variables by elimination. Compare and choose an appropriate method for solving systems of linear equations.

Solving Linear Systems by Linear Combinations (Elimination)

Solving a System of Equations in Two Variables by the Addition Method

SYSTEMS OF LINEAR EQUATIONS

Systems of linear equations substitution and elimination

Solving Systems of Linear Equations in 3 Variables.

Systems of Equations Solve by Graphing.

Section Solving Linear Systems Algebraically

6.3 Using Elimination to Solve Systems

Example 2B: Solving Linear Systems by Elimination

1-2 Solving Linear Systems

SOLVING SYSTEMS OF EQUATIONS.

Solving Systems by ELIMINATION

Chapter 5 Review.

The Substitution Method

Systems of three equations with three variables are often called 3-by-3 systems. In general, to find a single solution to any system of equations,

SOLVING SYSTEMS OF EQUATIONS.

SOLVING SYSTEMS OF EQUATIONS.

Presentation transcript:

Solving Systems of Linear Equations in Two Variables: When you have two equations, each with x and y, and you figure out one value for x and one value for y that will make BOTH equations true.

Three methods of solving systems: Graphing Method Substitution Method Elimination Method

Graphing Method Solve each equation for y, then graph each equation on a rectangular coordinate plane, then observe where the two lines intersect. The coordinates of the intersection point are the solutions of the system. Benefit: very easy to do Drawback :requires graph paper might be imprecise

Example: Solve by graphing : 2x + 3y = 7 - x + 2y = 14 (Go to Sketchpad sketch)

Three methods of solving systems: Graphing Method Substitution Method Elimination Method

In both of the next two methods, the Substitution Method and the Elimination Method, the process will involve the sub- goal of “getting rid of” one of the two variables, in order to form an equivalent equation in ONE variable (remember, it is easy to solve a linear equation in one variable!). After you solve for the one variable, you then plug the solution back into either of the original equations, and solve for the other variable.

Substitution Method In one of the equations, solve for one of the variables, either “ y = some expression with x” or “ x = some expression with y”. Then, substitute that new expression into the other equation, thereby getting rid of one of the variables. Then, simply solve the linear equation for the remaining variable.

Example: Solve by substitution : 2x + 3y = 7 and – x + 2y = 14

Elimination Method Multiply both sides of one (or both) equation(s) by the same number(s) in order to get the coefficients of one of the variables in each equation to be OPPOSITES (like 12y and -12y). Then, add the two equations to form a new equivalent expression in ONE variable, since the other variable has been “eliminated”. Now, solve the linear equation for the remaining variable.

Example: Solve by elimination : 2x + 3y = 7 and – x + 2y = 14

When does each method work best? Graphing Method good if you have graph paper AND if your solution does not have to be precise Substitution Method good if one of the variables has a coefficient of (invisible) 1, like 6x + y = 15 Elimination Method good if the coefficients of one of the variables divides evenly into the same variable’s coefficient in the other equation, like 3x + 5y = 9, and -2x + 10y = -8