Problem of the Day y= x – 7 2x – 6y = 12

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Presentation transcript:

Problem of the Day y= - 1 2 x – 7 2x – 6y = 12 Solve the following system algebraically, using substitution: y= - 1 2 x – 7 2x – 6y = 12

Solving Algebraically by Elimination I sure do love that trusty substitution! Look for a pair of matching opposites x + 3y = 8 6x – 3y = 27 + 7x = 35 7 But sometimes there’s an easier way! 7 x + 3y = 8 x = 5 5 + 3y = 8 (5, 1) 3y = 3 y = 1

Try shoveling a sidewalk with that thing buddy! Problem of the Day y= - 1 2 x – 7 2x – 6y = 12 What the deuce!? Mwahahahaha! Try shoveling a sidewalk with that thing buddy!

4( ) 2x + y = 3 7x – 4y = 18 8x + 4y = 12 7x – 4y = 18 Find an LCM Anyway, where were we? If you don’t have matching opposites, you can make them match. 4( ) 2x + y = 3 7x – 4y = 18 8x + 4y = 12 7x – 4y = 18 Find an LCM to distribute

Steps to Solving by Elimination Look for equal opposites or a pair that’s easy to manipulate Step 1 Distribute the coefficient you need across one or both equations to make equal opposites Step 2 Step 3 Add equations together and cancel pair Step 4 Solve for one variable Plug answer back in to find other variable Step 5

Practice 3x + 4y = 1 2x + 4y = 6 3x + 2y = -1 4x – 5y = -32

Solving Equations Algebraically Using Elimination Look for ___________________________________________________ x + 3y = 8 6x – 3y = 27 If you don’t have matching opposites, you can make them match: _________________________ ________________________________________________________________________ 2x + y = 3 7x – 4y = 18 Steps to solving systems by ELIMINATION: Step 1: _______________________________________________________________________ _______________________________________________________________________ Step 2: _______________________________________________________________________ Step 3: _______________________________________________________________________ Step 4: _______________________________________________________________________ Step 5 : _______________________________________________________________________ 3x + 4y = 1 3x + 2y = -1 2x + 4y = 6 4x – 5y = -32