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3) Special case

3) Special case. x = 3 – y x + y = 7. Step 1 : Solve an equation for one variable. The first equation is already solved for x!. Step 2 : Substitute. x + y = 7 ( 3 – y ) + y = 7. 3 = 7 The variables were eliminated!! This is a special case. Does 3 = 7? FALSE!.

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3) Special case

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  1. 3) Special case x = 3 – y x + y = 7 Step 1: Solve an equation for one variable. The first equation is already solved for x! Step 2: Substitute x + y = 7 (3 – y) + y = 7 3 = 7 The variables were eliminated!! This is a special case. Does 3 = 7? FALSE! Step 3: Solve the equation. When the result is FALSE, the answer is NO SOLUTIONS.

  2. 3) Special Case 2x + y = 4 4x + 2y = 8 Step 1: Solve an equation for one variable. The first equation is easiest to solved for y! y = -2x + 4 4x + 2y = 8 4x + 2(-2x + 4) = 8 Step 2: Substitute 4x – 4x + 8 = 8 8 = 8 This is also a special case. Does 8 = 8? TRUE! Step 3: Solve the equation. When the result is TRUE, the answer is INFINITELY MANY SOLUTIONS.

  3. You Try: 2. 6x – y = 31 4x + 3y = 17 1. x + 2y = 2 5x - 3y = -29

  4. Homework Pg 313 #2 to 16 even Pg 314 #32, 34 (do not graph)

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