In Example 3, change the constant to the right of the = sign in the first equation from −1 to −3, change the constant to the right of the = sign in the third equation from 9 to 11, and then solve the resulting system of equations.

Data from Example 3

Solve the following system by determinants.

Substituting in each of the original equations shows that the solution checks:

After the values of x and y were determined, we could have evaluated z by substituting the values of x and y into one of the original equations.

constants coefficients constants y = = 325 5 x = 462 - 162 3x + 2y 5z = -1 2x - 3y z = 11 5x - 2y + 7z = 9 = 11 -3 9 -2 7 11 -1 9 7 -162 2-5 2 -3 -1 5-2 75-2 77 27 - 2 2-5 -1 -1 11 -3 9 -2 325 21 18 + 110-135 +2 154 -63 10+ 2075-6-28 5 3 2 2-3 + 11 9 evaluate the denominator first; if it is zero, there is no need to evaluate the numerator - = -174 - 162 || denominator = -162 from solution for x 29 27 231 +590 + 275 + 27 + 14 - 162