how do you solve:
r + s + 2t - u = -3
2r + 3s + 3t + u = 2
4r + 2s - t + u = 5
s + 2t + 2u = 7
Get rid of the 2r by multiplying the 1st eq.
temporarily by -2 and adding it to the 2nd eq.
-2[ r + s + 2t - u = -3
1[2r + 3s + 3t + u = 2
4r + 2s - t + u = 5
s + 2t + 2u = 7
r + s + 2t - u = -3
s - t + 3u = 8
4r + 2s - t + u = 5
s + 2t + 2u = 7
Get rid of the 4r by multiplying the 1st eq.
temporarily by -4 and adding it to the 3rd eq.
-4[ r + s + 2t - u = -3
s - t + 3u = 8
1[4r + 2s - t + u = 5
s + 2t + 2u = 7
r + s + 2t - u = -3
s - t + 3u = 8
-2s - 9t + 5u = 17
s + 2t + 2u = 7
Get rid of the -2s by multiplying the 2nd eq.
temporarily by 2 and adding it to the 3rd eq.
r + s + 2t - u = -3
2[ s - t + 3u = 8
1[-2s - 9t + 5u = 17
s + 2t + 2u = 7
r + s + 2t - u = -3
s - t + 3u = 8
-11t + 11u = 33
s + 2t + 2u = 7
Notice that the third equation can be divided
through by -11. That will make things easier.
r + s + 2t - u = -3
s - t + 3u = 8
t - u = -3
s + 2t + 2u = 7
Get rid of the s in the bottom equation by
multiplying the 2nd eq. temporarily by -1 and
adding it to the 4th eq.
r + s + 2t - u = -3
-1[s - t + 3u = 8
t - u = -3
1[s + 2t + 2u = 7
r + s + 2t - u = -3
s - t + 3u = 8
t - u = -3
3t - u = -1
Getr rid of the 3t by multiplying the 3rd eq.
temporarily by -3 and adding it to the 4th eq.
r + s + 2t - u = -3
s - t + 3u = 8
-3[ t - u = -3
1[3t - u = -1
r + s + 2t - u = -3
s - t + 3u = 8
t - u = -3
2u = 8
Divide the 4th equation through by 2
r + s + 2t - u = -3
s - t + 3u = 8
t - u = -3
u = 4
The 4th equation tells us the value of u,
which is 4. Now we're ready to do back-
substitution:
Substitute u = 4 into the 3rd
equation:
t - u = -3
t - 4 = -3
t = 1
Substitute t = 1 and u = 4 into the 2nd
equation:
s - t + 3u = 8
s - 1 + 3(4) = 8
s - 1 + 12 = 8
s + 11 = 8
s = -3
Substitute s = -3, t = 1 and u = 4 into the 1st
equation:
r + s + 2t - u = -3
r + (-3) + 2(1) - (4) = -3
r - 3 + 2 - 4 = -3
r - 5 = -3
r = 2
So the solution is
(r, s, t, u) = (2, -3, 1, 4)
Edwin