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marshall27 [118]
2 years ago
15

Solve the system using substitution.

Mathematics
1 answer:
GaryK [48]2 years ago
4 0

Answer: x = 7, y = -3, z = 1

<u>Step-by-step explanation:</u>

EQ 1:    3x + 4y - z      =        8     <em>solve for z</em>

            <u>             +z  -8 </u>    <u>+z - 8 </u>

            3x + 4y - 8      =  z

EQ 3:   5x + y - 2z = 30      <em>substitute 3x + 4y - 8 for z and solve for x</em>

           5x + y - 2(3x + 4y - 8) = 30

           5x + y  - 6x - 8y + 16 = 30

                          -x - 7y + 16 = 30

                         <u>              -16 </u>  <u>-16 </u>

                         -x - 7y         = 14

                       <u>       +7y       </u>    <u>+7y  </u>  

                        -x                = 7y + 14

                         x                = -7y - 14

EQ 2:   x - 5y + 2z = 24    <em>substitute 3x+4y - 8 for z and -7y - 14 for x</em>

           (-7y - 14) - 5y + 2(3x + 4y - 8) = 24

             -7y - 14 - 5y + 6(-7y - 14) + 8y - 16 = 24

             -7y - 14 - 5y  - 42y - 84 + 8y - 16 = 24

                           -46y - 114 =  24

                            <u>        +114 </u>  <u>+114 </u>

                               -46y      = 138

                              <u>÷-46       </u>  <u>÷-46 </u>

                                     y    =  -3

x = -7y - 14

  = -7(-3) - 14

  = 21 - 14

  = 7

z = 3x + 4y - 8

  = 3(7) + 4(-3) - 8

  = 21 - 12 - 8

  = 1

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