3. Explain how you would solve this equation using your graphing calculator and then give the solution. Be sure that you write the steps clearly.
2x – 3y = 8
5x + 4y = 11
Step One: Create a 2X2 matrix with the coefficiants of the unknown terms,
we will call this matrix A.
[[2, -3]
[5, 4 ]]
Step Two: Calculate the determinant of the matrix A using the
det() function, the determinat of matrix A is 23.
Step Three: Make two new 2X2 matrixes based on our first one, but we
substitute one collum with the known numbers (8 and 11).
We get these, which will be denoted as matrices B and C
respectivly.
[[8, -3] [[2, 8]
[11, 4 ]] and [5, 11]]
Step Four: To find our first unkown term, (x), we caluate the determinant of
matrix B and divide it be determinant of matrix A. The determinat of matrix B is 65. So unknown X = 65 / 23.
Step Five: We find our second unkown term (y) in the same way.
The determinant of matrix C is -18. So Y = -18 / 23.