Solving 2 x 2 Determinants

Category: Algebra

"Published in Newark, California"

Solve the following systems of equations by determinants:

                                        x - 2y = 7

                                        3x - y = 11

Solution:

The first thing that we have to do is to write the determinants for D_x, D_y, and D from the given two linear equations. Determinant is a value associated with square matrix. Matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. Consider the given equations


                                        x - 2y = 7

                                        3x - y = 11

To write the determinant of D, consider the coefficients of x and y as follows

To write the determinant of D_x, replace the coefficients of x with the coefficients of the right side of the equation as follows

To write the determinant of D_y, replace the coefficients of y with the coefficients of the right side of the equation as follows

Next, solve for the value of x as follows

Finally, solve for the value of y as follows

Note: To get the value of a 2 x 2 Matrix, principal diagonal (top left term times bottom right term) minus secondary diagonal (bottom left term times top right term).

Check: To see if you got the correct answers, substitute the values of x and y to either of the two given equations as follows

                                        x - 2y = 7

                                     3 - 2(-2) = 7

                                         3 + 4 = 7

                                               7 = 7