A mathematical array is also called a matrix, and is a set of columns and rows that represents a system of equations. A system of equations is a series that uses the same variables in each equation. For example, [3x + 2y = 19] and [2x + y = 11] form a two-equation system. Such equations can be drawn as a matrix that contains the coefficients of each variable.

Write a system of equations: [2x + y + z = 18], [x + y + z = 15], and [3x - z + y = 7]. Write each equation on a separate line and number them 1, 2 and 3.

Draw a square about 4-by-4 inches and divide it into four columns and three rows. Make each column big enough to contain a two-digit number, and separate the fourth column from the others by a dotted line rather than a solid line.

Write the coefficients of x in the first cell of each row. The first row should correspond to equation 1, the second to equation 2 and the third to equation 3, so the values for the cells are 2, 1 and 3. Do the same in the second cell of each row for the coefficients of y, then in the third row for the coefficients of z.

Finish your matrix by writing the constants in the final cell of each row. In this case, the values to the right of the equal sign are 18, 15 and 7. If there are variables on the right side, use basic algebra with each equation so that the variables are all to the left of the equal sign and constants are to the right.

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