What is the solution to this system of equations? x+3y−z=6 4x−2y+2z=−10 6x+z=−12 (−4, 0, 12) (0, −2, −12) (2, 1, −3) (−3, 5, 6)

Solution :  (− 3, 5, 6)

Step-by-step explanation:

We have the following system of equations that we have to solve for,

To solve this problem we can start by writing the matrix with their respective coefficients --- (1)

Now we can reduce this to row echelon form, receiving our solution --- (2)

Swap row 1 and 3,

Cancel leading coefficient in row 3,

Swap row 2 and 3

Cancel leading coefficient in row 3

At this point you can see that we have to cancel the leading coefficient in each row, to row echelon form. Continuing this pattern we have the following matrix,

As you can see, x = - 3, y = 5, and z = 6, giving us a solution of (− 3, 5, 6). This is the fourth option.

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step-by-step explanation:

y = 2x

step-by-step explanation:

if you divide each number in the sequence, you'll see that they all have a multiple factor of 2. each number in the series, and any other numbers which may continue, will be multiplied by 2. therefore, y is the next number in the sequence, and x is the current one, so, our formula will be y = 2x.