Answer:
c) (-3, -1, -2)
Explanation:
It is convenient to use a graphing calculator's matrix functions to solve a set of equations of this sort. The attachment shows the use of a TI-84 for the purpose.
(x, y, z) = (-3, -1, -2) . . . . . corresponds to selection c)
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Solution by hand
It is often easiest to solve a set of equations like this by elimination. Here, we find the y-coefficients are multiples of each other, so it is convenient to eliminate y from the equations.
Adding twice the second equation to the first, we have ...
... -7x +7z = 7 ⇒ x -z = -1
Adding twice the first to the third, we have ...
... 10x -7z = -16
The first of these reduced equations can be written to give an expression for x:
... x = z -1
And this can be used in the second of the reduced equations to find z:
... 10(z -1) -7z = -16
... 3z = -6 . . . . . eliminate parentheses, add 10
... z = -2 . . . . . .divide by the coefficient of z
Then x = -2-1 = -3
Substituting into the 2nd of the original equations gives ...
... -5(-3) -2y +6(-2) = 5
... y = (15 -12 -5)/2 = -1
So, the solution by this method is (x, y, z) = (-3, -1, -2).
