how do I solve this problem with calculator: 3x+-2y=12, 6x+4y=-3

I do not know which calculator you are using, but I have a more recent TI-84 Plus CE. If you have any Texas Instrument that is TI83 or higher, I believe the process is more or less the same. I had to do this once, and I might as well just solve the system, to be honest.

 

1. Press 2nd+x^-1

 

For me, any secondary function is in blue, so you know as the user that you must press the 2nd button to access those features. You must press the 2nd button first and then the \(x^{-1}\) next. The \(x^{-1}\) is directly below the math button and directly above the \(x^2\) key. Upon doing this operation, the menu before you should look like the following:
 

1: [A]

2: [B]

3: [C]

4: [D]

...

 

 

2. Press the Right Navigational Arrow Twice

 

Upon doing this action, "Edit," in the top center area of the screen, should be fully enclosed. The menu should look the same as above.

 

3. Press Enter

 

Your matrix should now open up. The menu should look something like this:
 

Matrix[A]   x

[ 0              ]

 

Now, we must configure the matrix so that it fits this problem. In this case a 2x3 matrix is appropriate. 

 

Matrix[A] 2 x3

[ 0   0   0  ]

[  0  0   0  ]

 

4. Input Coefficient of Variables or Constants into Matrix.

 

For the example given, we have an equation in the form of \(Ax+By=C\). You would put the value of A, B, and C into the first row of the matrix. In this case, A=3, B=-2, and C=12. Be sure to enter this in order alphabetically in the row

 

Do the same thing with the second equation, too. A=6, B=4, and C=-3. Upon entering this information into the second row in alphabetic order of the variables, you should see the following:
 

Matrix[A] 2 x3

 

[  3   -2   12]

[  6   -4    -3]

 

If you see this on your calculator, then you have correctly inputted the values into the matrix, and you can move on to the next step.

 

4. Press 2nd + mode

 

You should see the home screen again. This is where you do the normal operations (like addition and multiplication, for example). Be sure to press the 2nd button first. 

 

5. Do Step 1 Again

 

6. Press the Right Navigational Arrow Once

 

In step 2, "edit" was the word that was enclosed. Now, "Math" should be enclosed at the top of the screen.

 

7. Press Alpha + apps

 

Alpha is a green key that one must press to access the terciary functions. Be sure to press alpha first. Then, press apps. Now, your homescreen should pop up again. You should see the following:

 

rref(

 

You don't have to worry about what rref is, but it stands for reduced row echelon form. This will simplify the matrix. Now, we must tell the calculator which matrix to apply it to.

 

8. Do Step 1 Again

 

9. Press Enter Twice

 

Now, something should appear on your homescreen. It should look like this:

 

rref([A]

              [ 1 0  1.75]

              [ 0 1  -3.375]

 

You're done now because the calculator has, in a cryptic manner, given you the solutions to this system of equations. Just know that the rightmost number is the numerical value of the variable that satisfies both equations. In this case, x=1.75 and y=-3.375

 

You're done. If you have any questions, ask!