Solve for [x,y] using Gause-Jordan elimination for this system: 4X-6Y=7 X+3Y=5?

Question

What is the procedure for the solving of the 2X2 matrix?

Answer 1

First construct the matrices

So frickin hard to write things like this when Yahoo throws out all the spaces. I'll try

[4 -6] [7]
[1 3] [5]

At this point there are a number of ways to go, but you usually look for the easy operations. What you want to do is eliminate one variable from one of the equations and then the other variable from the other equation. In this case, you could divide the first equation by 2 and add it to the second one.

Divide:
[2 -3] [3.5]
[1 3] [5]

Add:
[2 -3] [3.5]
[3 0] [8.5]

Now multiply the second equation by -2/3 and add it to the first

Multiply:
[2 -3] [3.5]
[-2 0] [-5.6666...]

Add:
[0 -3] [-2.16666...]
[-2 0] [-5.6666...]

Now simply multiply or divide by whatever is necessary to get the left side to have only ones

[0 1] [0.72222...]
[1 0] [2.83333...]

Check:
4*2.833333 - 6*0.72222 = 7

Check!

Answer 2

4x-6y=7
x+3y=5
you want to subtract one equation from the other to get
x+Ay=B
y=C

for example, row 1- 4*row2
4x-6y=7
-(4x+12y=20)
-18y=-13

Answer 3

4x-6y=7
double second equation=
14x+6y=10
add them together
18x=17
x=17/18

Answer 4

Punch it into your good old ti 84 and wahlah!