Page:Elementary algebra (1896).djvu/463

445 Rh Ex. Solve x+2y+4+3z-13=0, 2x+ y+ z- 7=0, 3x+4y+32-21=0.

We have

or

whence x=1, y= 3, and z= 2.

Explanation. The denominator of x is a determinant formed by taking the coefficients in each column except that of x. In the same manner for the denominators of y and z we omit the columns of coefficients of y and z. The last determinant is formed by taking the three columns of coefficients of x, y, and z.

553. Suppose we have the system of four homogeneous linear equations

a_1 x + b_1 y + c_1 z + d_1 u = 0,

a_2 x + b_2 y + c_2 z + d_2 u = 0,

a_3 x + b_3 y + c_3 z + d_3 u = 0,

a_4 x + b_4 y + c_4 z + d_4 u = 0,

From the last three of these, we have, as in the preceding article,

Substituting in the first equation, the eliminant is