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Pearson Algebra 2 Common Core, 2011 View details

5. Systems With Three Variables

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Exercise 41 Page 172

Can you manipulate the coefficients of any variable terms such that they could be eliminated?

(0,2,-3)

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The given system consists of equations of planes. Notice that the coefficient of z in the first equation is the additive inverse of the coefficients of z in the second and third equations; they will add to be 0. Therefore, let's use the Elimination Method to find a solution to this system. 4x-y + z=-5 & (I) - x+y - z=5 & (II) 2x - z-1=y & (III) We can start by adding the first equation to the second and third equations to eliminate the z-terms.

4x-y+z=-5 & (I) - x+y-z=5 & (II) 2x-z-1=y & (III)

(II), (III): Add (I)

4x-y+z=-5 - x+y-z+( 4x-y+z)=5+( -5) 2x-z-1+( 4x-y+z)=y+( -5)

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(II), (III): Simplify

(II), (III): Remove parentheses

4x-y+z=-5 - x+y-z+4x-y+z=5-5 2x-z-1+4x-y+z=y-5

(II), (III): Add and subtract terms

4x-y+z=-5 3x=0 6x-1-y=y-5

DivEqn

(II): .LHS /3.=.RHS /3.

4x-y+z=-5 x=0 6x-1-y=y-5