3.6 part 1 c - =-19 3 4 15 3 2 4 3 3 z y x z y x z y x...

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1 Warm-up Solve each system. 1) 2) - = + = - 7 2 11 2 y x y x - = - = + - 14 12 2 8 6 y x y x Solving 3 Variable Systems by Elimination Objective: -to solve 3 variable systems by elimination one solution- planes intersect at one common point no solution- no point lies in all three planes. infinite number of solutions planes intersect at all the points along a common line. Solving by Elimination -When solving a system of three equations in three variables you work with the equations in pairs. You will use one of the equations twice . Step 1: Pair the equations and eliminate y, because the y terms are already additive inverses. ADD 1 and 2 (call that 4), then ADD 2 and 3 (call that 5)
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Unformatted text preview: = +-19 3 4 15 3 2 4 3 3 z y x z y x z y x Solving by Elimination Step 2: Now write 4 and 5 as a system. Solve for x and z. 3x+2z = 11 x=5, z = 2 =-= + 34 2 6 11 2 3 z x z x 2 Solving by Elimination Step 3: Substitute values for x and z into one of the original equations (1,2, or 3) and solve for y. x=5, z=-2 x – 3y + 3z = -4 You try! =---= +-=-+ 1 2 3 5 2 z y x z y x z y x Solving by Elimination You may have to multiply an equation by a nonzero number in order to eliminate. For example: =-+ = + + =-+ 12 2 6 15 16 2 4 5 2 z y x z y x z y x Homework p. 157 # 1-9...
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