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# Chapter 6: Systems of Equations and Inequalities

We will be finding the point of intersection for two equations and the overlapping area of two inequalities.

by

Tweet## Paulina Villalobos

on 10 January 2017#### Transcript of Chapter 6: Systems of Equations and Inequalities

Chapter 6A: Systems of Equations Verifying Solutions Example Tell whether the ordered pair is a solution of the given system.

(-2,2); x + 3y = 4 and -x + y = 2 Steps to Success:

1) Solve for one of the variables in at least one equation

2) Substitute the resulting expression into the other equation

3) Solve that equation to get the value of the first variable

4) Substitute that value into one of the original equations and solve for the other variable

5) Write the values from Steps 3 and 4 as an ordered pair The Substitution Method 4y - 5x = 9

x - 4y = 11 Example: Steps to Success:

1) Write the system so that like terms are aligned

2) Eliminate one of the variables

3) Solve for the variable not eliminated in Step 2

4) Substitute the value of the variable into one of the original equations and solve for the other variable

5) Write the answers from Steps 3 and 4 as an ordered pair The Elimination Method x + y = 12

2x + 5y = 27 Classwork: pg. 332 #2-4, 9-11 Example:

x + 4y = 6

x + y = 3 Example: x + 2y = 11

-3x + y = -5 Classwork: Pg. 340 #1,3, 6, 9, 13, 14, 15, 19, 20 Pg.347 #1, 5, 6, 7, 8, 9, 11, 17 Solving Special Systems: Infinitely many solution -> dealing with the same line

No solution -> Parallel lines Example: Solve the system using one of the two methods y = x - 1

-x + y = 2 Classwork: Pg.353 #12-18 All I Do Is Solve Review: pg. 381 #13, 15, 17 Answers: 13) (-9, -6)

15) (-1, 6)

17) (-5, 2) What kind of lines are they? 1) same lines

2) parallel lines

3) intersecting lines

Full transcript(-2,2); x + 3y = 4 and -x + y = 2 Steps to Success:

1) Solve for one of the variables in at least one equation

2) Substitute the resulting expression into the other equation

3) Solve that equation to get the value of the first variable

4) Substitute that value into one of the original equations and solve for the other variable

5) Write the values from Steps 3 and 4 as an ordered pair The Substitution Method 4y - 5x = 9

x - 4y = 11 Example: Steps to Success:

1) Write the system so that like terms are aligned

2) Eliminate one of the variables

3) Solve for the variable not eliminated in Step 2

4) Substitute the value of the variable into one of the original equations and solve for the other variable

5) Write the answers from Steps 3 and 4 as an ordered pair The Elimination Method x + y = 12

2x + 5y = 27 Classwork: pg. 332 #2-4, 9-11 Example:

x + 4y = 6

x + y = 3 Example: x + 2y = 11

-3x + y = -5 Classwork: Pg. 340 #1,3, 6, 9, 13, 14, 15, 19, 20 Pg.347 #1, 5, 6, 7, 8, 9, 11, 17 Solving Special Systems: Infinitely many solution -> dealing with the same line

No solution -> Parallel lines Example: Solve the system using one of the two methods y = x - 1

-x + y = 2 Classwork: Pg.353 #12-18 All I Do Is Solve Review: pg. 381 #13, 15, 17 Answers: 13) (-9, -6)

15) (-1, 6)

17) (-5, 2) What kind of lines are they? 1) same lines

2) parallel lines

3) intersecting lines