What is the solution to the system? x+y-z=0
3x-y+z=4
5x+z=7

D. (x, y, z) = (1, 1, 2). That is:

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Step-by-step explanation:

Step One: Make sure that the first coefficient of the first row is 1. In this case, the coefficient of in the first row is already 1.

Step Two: Using row 1, eliminate the first unknown of row 1 in the rest of the rows. For example, to eliminate from row 2, multiply row 1 by the opposite of the coefficient of in row 2 and add that multiple to row 2. The coefficient of in row 2 is . Thus, multiply row 1 by to get its multiple:

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Add this multiple to row 2 to eliminate in that row:

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Similarly, for the third row, multiply row 1 by to get:

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Do not replace the initial row 1 with this multiple.

Add that multiple to row 3 to get:

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After applying step one and two to all three rows, the system now resembles the following:

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Ignore the first row and apply step one and two to the second and third row of this new system.

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Step One: Make sure that the first coefficient of the first row is 1.

Multiply the first row by the opposite reciprocal of its first coefficient.

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Row 1 is now .

Step Two: Using row 1, eliminate the first unknown of row 1 in the rest of the rows.

The coefficient of in row 2 is currently . Multiply row 1 by   to get:

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Do not replace the initial row 1 with this multiple.

Add this multiple to row 2:

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The system is now:

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Include the row that was previously ignored:

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This system is now in a staircase form called Row-Echelon Form. The length of the rows decreases from the top to the bottom. The first coefficient in each row is all . Find the value of each unknown by solving the row on the bottom and substituting back into previous rows.

From the third row: .

Substitute back into row 2:

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Substitute and to row 1:

.

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In other words,

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by definition, an arc subtended by a central angle of some given measure has the same measure. so .