We have the simultaneous equations

-x + 2y = 1.5 ...(1)

2x - 4y = 3 ...(2)

Looking at the two matrices we see that 2*(1) = -2x + 4y = 3

=> 2x - 4y = -3

Comparing to (2) we see that 2x - 4y = 3 and 2x - 4y = -3

This is not possible. Therefore it is not possible to solve the equations. There is no use of using the matrix method as it would not yield a solution

**The set of equations cannot give a solution.**

You can use the scientific TI-83 or TI-84 to find the solution of this system of equations.

Press 2nd then X^-1 button.

Set up your matrix by 2 x 3

enter the values as following for your variables on left side and constant on the right side in the martrix as following:

-1 2 1.5

2 -4 3

Then press 2nd MODE

Then go back to 2nd Matrix

Go to MATH

Go to B: rref ( press ENTER

Go Back to 2nd MATRIX

Press enter on [A] matrix

Then press ENTER again

The solution for this matrix is

0, 1

There is no real solution to this matrix, since the value of one of the variable is zero.