page 77

Thus we see that the solution of a system of simultaneous first-degree equations can be written as ratios of determinants in which the denominator is the determinant made up of coefficients of x and y in the order in which they appear in the equations, while the numerator for x is the same determinant with the coefficients of x replaced by the constants, and the numerator for y is the determinant of the denominator with the coefficients of y replaced by the constants.

This technique is called Cramer's Rule. The common denominator is called the determinant of the system.

Example 1. Solve by determinants:

3x + 2y = 5
x - 7y = 2

Solution: We first evaluate the determinant in the denominator (the determinant of the system), as follows:

Since this determinant is not zero, the system has the unique solution:

COVER PAGE

TABLE OF CONTENTS

INDEX

PROBLEMS FOR THIS SECTION

page 77

Wednesday, June 10, 1998