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joja [24]
3 years ago
10

Solve using addition method 3x-3y+2z=7 3x+y-3z=-5 7x-y-2z=0

Mathematics
1 answer:
frozen [14]3 years ago
6 0
3x - 3y + 2z = 7  
3x + 1y - 3z = -5  ⇒ 6x - 2y - 1z = 2 ⇒ 42x - 14y -   7z = 14
7x  - 1y - 2z = 0   ⇒ 7x - 1y - 2z = 0 ⇒ <u>42x -   6y - 12z = 0    </u>
                                                                      -20y - 19z = 14
                                                            -20y + 20y - 19z = 14 + 20y
                            <u />                                                   <u>-19z</u> = <u>14 + 20y</u>
                                                                                -19         -19
                                                                                    z = -14/19 - 1 1/19y
                                         3x - 3y + 2(-14/19 - 1 1/19y) = 7
                                              3x - 3y - 1 9/19 - 2 2/19y = 7
                                                     3x - 5 2/19y - 1 9/19 = 7
                                                     <u>      +1 9/19  +1 9/19        </u>
                                                                   3x - 5 2/19y = 8 9/19
                                                            3x - 3x - 5 2/19y = 8 9/19 - 3x
                             <u />                                            <u>-5 2/19y</u> = <u>8 9/19 - 3x</u> 
                                                                         -5 2/19        -5 2/19
                                                                                     y = -1 64/97 + 57/97x
             3x - 3(-1 64/97 + 57/97x) + 2(-14/19 - 1 1/19y) = 7
                    3x + 4 95/97 + 1 74/97x - 1 9/19 - 2 2/19y = 7
                               4 74/97x - 2 2/19y + 3.5056972328 = 7
                               <u>                                -3.5056972328   -3.5056972328</u>
                                                          4 74/97x - 2 2/19y = 3.494302767
                                          4 74/97x + 2 2/19y - 2 2/19y = 3.494302767 + 22/19y
                                                                          <u>4 74/97x</u> = <u>3.494302767 + 2 2/19</u>
                                                                           4 74/97               4 74/97
                                                               x = 0.7336523126 + 0.4420141262y
3(0.733652316 + 0.4420141262y) - 3(-1 64/97 + 57/97x) + 2(-14/19 - 1 1/19y)=7
          2.200956948 + 1.326042379y + 4 95/97 - 1 74/97x - 1 9/19 - 2 2/19y = 7                             -1 74/97x - 0.7792207789y + 5.706654181 = 7
                         <u>                                               -5.706654181    -5.70665418</u>
                                                     -1 74/97x - 0.7792207789y = 1.293345820
(x, y, z) = (0.733652316 + 0.4420141262, -1 64/97 + 57/97x, -14/19 - 1 1/19y)

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