Summary: EXAMPLES OF THE "STANDARD" METHOD FOR SOLVING
LINEAR EQUATIONS
MATH2573H, SPRING 2012, UNIVERSITY OF MINNESOTA
GREG W. ANDERSON
A problem with a two-parameter family of solutions
w + 2x + 3y + 4z = 5
6w + 7x + 8y + 9z = 10
1 2 3 4 5
6 7 8 9 10
1 2 3 4 5
0 -5 -10 -15 -20
1 2 3 4 5
0 1 2 3 4
1 0 -1 -2 -3
0 1 2 3 4
w -y -2z = -3
x +2y +3z = 4
"pivot" "pivot" "free" "free"
Let y = s and z = t. Then:
w = y + 2z - 3 = s + 2t - 3 and x = -2y - 3z + 4 = -2s - 3t + 4.

Source: Anderson, Greg W. - School of Mathematics, University of Minnesota

Collections: Mathematics