Question

−x−4y+2z=

Answer 1

9514 1404 393

Answer:

  (x, y, z) = (8, 0, 3)

Step-by-step explanation:

Maybe you want to solve the system of equations represented by the augmented matrix ...

  $\left[\begin{array}{ccc|c}-1&-4&2&-2\\-1&3&2&-2\\1&9&-4&-4\end{array}\right]$

Your graphing calculator can provide the solution for you:

  (x, y, z) = (8, 0, 3)

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If you want to solve this by hand, it works reasonably well to make a plan based on the values of the coefficients. We notice only the y-coefficient differs in the first two equations, telling us that y=0. This immediately reduces the system to two equations in x and z. The x-coefficients are opposites, so we can easily eliminate x to find z.

You can subtract the first equation from the second to find the value of y.

  (-x +3y +2z) -(-x -4y +2z) = (-2) -(-2)

  7y = 0   ⇒   y = 0

Substituting for y in the first and third equations, you can add those together:

  (-x +2z) +(x -4z) = (-2) +(-4)

  -2z = -6   ⇒   z = 3

Substituting into the last equation gives ...

  x -4(3) = -4   ⇒   x = 8

Then the solution is (x, y, z) = (8, 0, 3).