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Intermediate Algebra Question!?
1. Solve the system of equations using the elimination method: Please show work.
1) x + 2y + z = 0
2) 3x + 2y - z = 4
3) -x + 2y + 3z = - 4
2. Solve the system of equations using the elimination method: Please show work
1) 3x + 3y + 3z = 12
2) 2x + 2y - z = - 4
3) -x + y - z = - 2
1 Answer
- mijota666Lv 49 years agoFavorite Answer
1.
1 2 1 _ 0
3 2 -1 _ 4
-1 2 3 _ -4
r2-3*r1 , r3+r1 ;
1 2 1 _ 0
0 -4 -4 _ 4
0 4 4 _ -4
r2/-4 , r3/4 ;
1 2 1 _ 0
0 1 1 _ -1
0 1 1 _ -1
r3-r2 ; r1-2*r2
1 0 -1 _ 2
0 1 1 _ -1
0 0 0 _ 0
should be infinite solutions , parameterize in terms of z ,
let z = t ; then x-t=2 , y+t=-1 , z=t
or {x, y, z} = {2+t, -1-t, t}
t=0 ; {x, y, z} = {2, -1, 0}
t=1 ; {x, y, z} = {3, -2, 1}
t=2 ; {x, y, z} = {4, -3, 2} etc
2.
3 3 3 _ 12
2 2 -1 _ -4
-1 1 -1 _ -2
r3/3 ;
1 1 1 _ 4
2 2 -1 _ -4
-1 1 -1 _ -2
r2-2*r1 , r3+r1 ;
1 1 1 _ 4
0 0 -3 _ -12
0 2 0 _ 2
swap r2&r3 ;
1 1 1 _ 4
0 2 0 _ 2
0 0 -3 _ -12
r2/2 , r3/-3 ;
1 1 1 _ 4
0 1 0 _ 1
0 0 1 _ 4
r1-r2 ;
1 0 1 _ 3
0 1 0 _ 1
0 0 1 _ 4
r1-r3 ;
1 0 0 _ -1
0 1 0 _ 1
0 0 1 _ 4
so x=-1 , y=1 , z=4
or {x, y, z} = {-1, 1, 4}
.
