Solve for x, y, and z.3x + 4y - 5z = -3-5x - 2y + 6z = 54x - 8y + 3z = -10a) (-3, 17, 4)b) (-2, -1, -3)c) (-3, -1, -2)d) (3, 2, 4)

c) (-3, -1, -2)

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).

step-by-step explanation:

50-38=12

step-by-step explanation: