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Algebra

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Solve the following system of linear equations:

2x - 3y + 6z = -12
5x + 2y - 8z = 29
7x + 6y + 4z = 49

First, I did elimination for the first two equations. I multiplied the first equation by two, and the second equation by 3.

4x - 6y + 12z = -24
+
15x + 6y - 24z = 87

That gets me:
19x - 12z = 63.

The next thing I have written down that the teacher told us is:

11x + 16z = 25

How did my teacher get to this point?
Thanks!

  • Algebra - ,

    combine twice the top one and the bottom one
    4 x - 6 y + 12 z = -24
    7 x + 6 y + 4 z = +49
    ------------------------
    11 x + 0 + 16 z = 25

  • Algebra - ,

    In the end
    x = 3
    y = 5
    z = -.5

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