In Example 3, change the + to − in the first equation and then solve the system of equations.

Data from Example 3

Solve the following system of equations by determinants:

First, note that the equations are in the proper form of Eqs. (5.4) for solution by determinants.] Next, set up the determinant for the denominator, which consists of the four coefficients in the system, written as shown. It is

For finding x, the determinant in the numerator is obtained from this determinant by replacing the first column by the constants that appear on the right sides of the equations. Thus, the numerator for the solution for x is

For finding y, the determinant in the numerator is obtained from the determinant of the denominator by replacing the second column by the constants that appear on the right sides of the equations. Thus, the numerator for the solution for y is

Now, set up the solutions for x and y using the determinants above:

Therefore, the solution to the system of equations is x = −1, y = 3. Substituting these values into the equations, we have

which shows that they check.

Transcribed Image Text:

2x + y = 1 5x2y-11