Systen of equation 3x-6y-3z=-3 ; -3x+2y-3z=17; x-4y-5z=11

(x, y, z) = (2, 4, -5)

Step-by-step explanation:

You can use the last equation to write an expression for x that can be substituted into the first two equations.

... x = 11 +4y +5z

... 3(11 +4y +5z) -6y -3z = -3 . . . . substitute into the first equation

... 6y +12z = -36 . . . . . . . . . . . . . simplify, subtract 33

... y + 2z = -6 . . . . . . . . . . . . . . . . divide by 6 to put in standard form

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... -3(11 +4y +5z) +2y -3z = 17 . . . . substitute into the second equation

... -10y -18z = 50 . . . . . . . . . . . . . simplify, add 33

... 5y +9z = -25 . . . . . . . . . . . . . . divide by -2 to put in standard form

Multiply the first of these equations by 5 and subtract the + 5(second.

... 5(y +2z) -(5y +9z) = 5(-6) -(-25)

... z = -5

You can use this in the first of the reduced equations:

... y + 2(-5) = -6

... y = 4 . . . . . . . . add 10

Then the expression for x will give that value:

... x = 11 +4(4) +5(-5)

... x = 2

The solution is (x, y, z) = (2, 4, -5).

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