#### Answer

The fastest method to solve a system of 3 linear equations using a graphical utility is by finding out the determinant of the matrix.

#### Work Step by Step

When a graphical utility is used for solving a system of 3 linear equations, then expressing the coefficients in the form of the matrix to obtain the determinant directly is quite simple because there are no complex and lengthy calculations involved.
The output is the value of the determinant of the matrix by which we can obtain the value of each variable.
Once the value of the determinant for each variable of the equation is obtained, the values for each variable can be easily calculated.