Systems of Equations: SOLVING BY SUBSTITUTION OR ELIMINATION

Recall: Steps to Solve Equations  Use Distributive property to get rid of parentheses  Combine like terms on each side of equals sign  “Move” variables to left of equals sign by adding or subtracting  “Move” constants to right of equals sign by adding or subtracting  Get variable by itself by either dividing or taking the root.

Solving Systems of Equations:  Solve by Graphing (we will discuss in next unit)  Solve by Substitution  Solve by Elimination

Solving Systems by Substitution:

Systems of Equations: Solve using Substitution

Example 2:

Solving Systems of Equations Using Elimination  To solve a system of equations using elimination, you add the equations together so that one variable is “eliminated”; you may have to multiply each equation by a value to have this occur.

Example 3:

Example 4:

Assignment: pp #13, 14, 16, 50, 58, 76 I WILL BE CHECKING ONE OF THESE FOR ACCURACY!!!

Bell Ringer: 8/26/15

Answers to Assignment:  13. (-2,1)50. (3, 3)  14. (3, -4)58. infinite solutions  16. a=-4, b=676. Gloria is correct.

Systems of Equations with 3 Variables  Recall: The three ways to solve systems of equations with 2 variables?  We can solve systems of equations with 3 variables in the same manner. However, graphing is difficult (because we are graphing in 3 dimensions). So what two ways remain to solve systems of equations with three variables?

Systems of Equations w/3 Var: Elimination Process  Step 1: Choose 2 equations and eliminate a variable. This is equation #4.  Step 2: Choose 1 of the equations from step 1 and the other equation you haven’t used and eliminate the same variable. This is equation #5.  Step 3: Use equations #4 and #5 to eliminate a variable. This will give you a value for 1 of the 3 variables.  Step 4: Use your answer in step 3 to substitute into either equation #4 or #5 to determine the other value of the variable in the equation.  Step 5: Use your answers from step 3 and step 4 to substitute into one of your original equations to solve for the final variable.

WOW THAT’S A LOT OF WORK FOR ONE PROBLEM!  So in this class, we will solve systems of equations with 3 variables using substitution.  Step 1: Find the value of one variable (may be given or may need to solve a simple equation to determine that value)  Step 2: Substitute that value into the equation that has 2 variables and determine the value of the variable in the equation.  Step 3: Substitute values found in Steps 1 and 2 into the equation with all three variables and find the remaining value.

Example:

Assignment:  Systems of Equations-Substitution Method: 3 Variables Handout  I WILL BE CHECKING ONE OF THESE FOR ACCURACY!