6-2 HOMEWORK 6-3 HOMEWORK 6-3: SOLVING SYSTEMS USING ELIMINATION Ms. Miller SOLVING SYSTEMS USING ELIMINATION Using the ________________, 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 __________ Elimination method variable opposites ELIMINATION BY ADDING STEP 2: Solve the equations for the remaining variable. STEP 1: Eliminate a variable in the system by adding the equations. STEP 3: Substitute the value of x into either equation and solve for y. STEP 4: Check your solution. ELIMINATION BY SUBTRACTING STEP 2: Solve the equations for the remaining variable. STEP 1: Eliminate a variable in the system by subtracting the equations. STEP 3: Substitute the value of x into either equation and solve for y. STEP 4: Check your solution. TRY THESE SOLVING SYSTEMS USING ELIMINATION In the beginning of the lesson, we saw that to ____________ a variable, its coefficients must have a _________ or ______________. 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 multiply difference SOLVE USING ELIMINATION STEP 2: Multiply the variable by a constant so that the equations will have opposite coefficients STEP 1: Choose a variable to eliminate. STEP 3: Proceed to solve by elimination STEP 4: Check your solution. SOLVE USING ELIMINATION STEP 2: Multiply the variable by a constant so that the equations will have opposite coefficients STEP 1: Choose a variable to eliminate. STEP 3: Proceed to solve by elimination STEP 4: Check your solution. TRY THESE Infinitely Many Solutions No Solution 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 TRY THESE x = multiple choice questions y = open-ended questions Number of Questions Points X = 35 Y = 3 A concessions stand sold a total of 138 small and large popcorns. A small popcorn costs $2.00, and a large popcorn $4.00. Total popcorn sales were $ How many large popcorns were sold? 1. Define variables 2. Create equations 3. Solve the system of equations 4. Check your solutions TRY THESE X = Small popcorns sold Y = large popcorns sold Number Sold Money Earned X = 43 Y = 95