SOLUTION: Can you help me solve this Using augmented matrices to solve the following 2 x 2 systems of equations. Show all work. 1. 3x + 4y = 11 x + 3y = 2

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Question 146738: Can you help me solve this Using augmented matrices to solve the following 2 x 2 systems of equations. Show all work.
1. 3x + 4y = 11
x + 3y = 2

Found 2 solutions by nerdybill, Alan3354:
Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
If you started with:
3x + 4y = 11
x + 3y = 2
.
The "coefficient matrix" is:
3 4
1 3
.
The determinant of the "coefficient matrix" is:
(3*3) - (1*4) = 9 -4 = 5
.
The 'x' matrix is:
11 4
2 3
.
The determinant of the 'x' matrix is:
(11*3)-(2*4) = 33 -8 = 25
.
The 'y' matrix is:
3 11
1 2
.
The determinant of the 'y' matrix is:
(2*3)-(1*11) = 6 -11 = -5
.
Solution for 'x' is "det of x"/"det of coefficient":
25/5 = 5
.
Solution for 'y' is "det of y"/"det of coefficient":
-5/5 = -1
.
Our solution is (x,y) = (5,-1)
.
To check, plug it back into:
x + 3y = 2
5 + 3(-1) = 2
5 - 3 = 2
2 = 2 (check)
and
3x + 4y = 11
3(5) + 4(-1) = 11
15 - 4 = 11
11 = 11 (check)

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
3x + 4y = 11
x + 3y = 2
3 4 -11
1 3 -2
Find the Determinant.
3 4
1 3
= 3*3-1*4
= 5
Ignore the x column
4 -11
3 -2
= 4*-2-(3*-11)
= 25
So x is 25/5
x = 5
Ignore the y column
3 -11
1 -2
= -(3*-2-(1*-11))
= -5
So y = -1
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