Question

-3x-2y-3z=5

x+2y-z=-19

-2x+y-2z=1

Answer 1

9514 1404 393

Answer:

(x, y, z) = (-9, -1, 8)

Explanation:

My calculator tells me the reduced row-echelon form of ...

`\left[\begin{array}ccc-3&-2&-3&5\\1&2&-1&-19\\-2&1&-2&1\end{array}\right]`

is ...

`\left[\begin{array}c1&0&0&-9\\0&1&0&-1\\0&0&1&8\end{array}\right]`

This means the solution is (x, y, z) = (-9, -1, 8).

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Additional comment

In case you haven't learned how to use your graphing calculator to solve matrix equations, you can solve this system easily as follows:

Subtract 2 times the first equation from 3 times the third equation. This eliminates the x and z terms and gives you the value of y. (y=-1)

Substitute that value into the first and second equations. This gives you two equations in the sum and difference of x and z. (You may need to divide the coefficients by the common factor.) Add these sum and difference equations to find one of the variables, then substitute to find the other.