Question

Using the inverse of:
2 1
-3 4
Find
2x+y=2
-3x+4y=1

Answer 1

It is supposed to be a matrix.
2, 1
-3, 4
but i donot know how to put the brackets. i used commas to separate the numbers

Answer 2

well, I will use gauss jordan, see the link I gave you.
2,1,1,0
-3,4,0,1

+1, .5 , .5, 0
-3, 4. , 0 , 1
multiply top by +3 and add to bottom
+1, .5 , .5 , 0
0 , 5.5, 1.5, 1
divide second row by 5.5
+1, .5 , .5 , 0
0 ,1.0, .273,.182
subtract half the second row from the first to get a new first
+1 , 0 , .364, -.091
0 , 1.0, .273, .182
so I think the inverse is
.364 , -.091
.273 , .182
multiply that by
2
1
and get
x = 2*.364 - 1* .091 = .637
y = 2*.273 +1 * .182 = .728
check
2*.637 + .728 = close enough to 2
-3*.637 + 4*.728 = close enough to 1

Answer 3

I have not inverted a matrix by hand for a while :)