Math

1.) Solve this system of linear equations. Write the final answer as an ordered pair (x, y, -3).

x - y + 2z = 22
3y - 8z = -9
z = -3

2.) Solve this system of linear equations. Write the final answer as an ordered pair (x, y, z).

2x + 4y + z = 1
x - 2y - 3z = 2
x + y - z = -1

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  1. using substitution,
    z = -3, so
    3y-8(-3) = -9
    3y = -33
    y = -11
    so,
    x-(-11)+2(-3) = 22
    x+11-6 = 22
    x = 17
    So the solution is (17,-11,-3)

    The other is not quite so simple, but

    since z = 1-2x-4y, we have
    x-2y-3(1-2x-4y) = 2
    x+y-(1-2x-4y) = -1
    or,
    7x+10y = 5
    3x+5y = 0
    So, since 5y = -3x, 10y = -6x and we have
    7x-6x = 5
    x = 5
    so, y = -3
    and z = 3

    solution is (5,-3,3)

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