 # 6-3: Solving systems Using Elimination

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6-3: Solving systems Using Elimination
Part 1

Solving Systems Using Elimination
Using the method, we will use Addition and Subtraction Properties of Equality to add or subtract equations to eliminate a ___________ in a system. First, look at the equations and see if the coefficients of a variable are __________ VARIABLE OPPOSITES

Elimination by adding What is the solution to the system
STEP 1: Eliminate a variable in the system by adding the equations. STEP 2: Solve the equations for the remaining variable. STEP 3: Substitute the value of x into either equation and solve for y. STEP 4: Solution to the system:

Elimination by subtracting
What is the solution to the system STEP 1: Eliminate a variable in the system by subtracting the equations. STEP 2: Solve the equations for the remaining variable.

STEP 3: Substitute the value of y into either equation and solve for x.
STEP 4: Solution to the system:

Try these

Homework: Sect. 6.3 p. 397-398 #’s 6-20 even

6-3: Solving systems Using Elimination
Part 2

Solving Systems Using Elimination
In yesterday’s lesson, we saw that to ____________ a variable, its coefficients must have a _________ or ______________ of zero. Sometimes, we have to ___________ one or both of the equations by a constant so that adding or subtracting the equations will eliminate a variable. ELIMINATE SUM DIFFERENCE MULTIPLY

Solving a System by Multiplying One Equation
What is the solution to the system STEP 1: Choose a variable to eliminate. STEP 2: Multiply the variable by a constant so that the equations will have opposite coefficients

STEP 3: Proceed to solve by elimination
STEP 4: Solution to the system:

Solving a System by Multiplying Both Equations
What is the solution to the system STEP 1: Choose a variable to eliminate. STEP 2: Multiply the variable by a constant so that the equations will have opposite coefficients

STEP 3: Proceed to solve by elimination
STEP 4: Solution to the system:

Examples: Try these! Infinitely Many Solutions

Try these Your math test has 38 questions and is worth 200 points. The test consists of multiple-choice questions worth 4 points each and open-ended questions worth 20 points each. How many of each type of question are there? 1. Define variables 2. Create equations 3. Solve the system of equations 4. Check your solutions x = multiple choice questions y = open-ended questions Number of Questions Points x = 35 y = 3

Homework: Sect. 6.3 p. 402-403 #’s 6-14 even, 18-20