SOLUTION: Express the solution in the form(x,y,z,w) 3x+y-z+2w=9 x+y+2z-w=10 x-y-z+3w=-2 -x+y-z+w=-6 Please show me how th get the corret answes I've been working on this problem for 2

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Express the solution in the form(x,y,z,w) 3x+y-z+2w=9 x+y+2z-w=10 x-y-z+3w=-2 -x+y-z+w=-6 Please show me how th get the corret answes I've been working on this problem for 2      Log On


   

Question 61537This question is from textbook Beginning and Intermediate Algebra
: Express the solution in the form(x,y,z,w)
3x+y-z+2w=9
x+y+2z-w=10
x-y-z+3w=-2
-x+y-z+w=-6
Please show me how th get the corret answes I've been working on this problem for 2 days now and it's due tomorrow someone pls help. This question is from textbook Beginning and Intermediate Algebra

Answer by asha(30) About Me  (Show Source):
You can put this solution on YOUR website!
3x+y-z+2w=9 eqn.1
x+y+2z-w=10 eqn.2
x-y-z+3w=-2 eqn.3
-x+y-z+w=-6 eqn.4
eqn3+eqn4 =-2z+4w =-8
taking out 2 as the common factor we get
-z+2w =-4 eqn.5
plugging value of -z+2w in eqn.1 we get
3x+y-4=9
3x+y =13 eqn.6
eqn.1-eqn.4 =4x +w=15 eqn.7
eqn.2 +eqn.4 =2y+z =4 eqn.8
eqn.5 +eqn.7 gives 2y+2w+4=4
2y +2w=4-4 =0
y +w =0
eqn.6 +eqn.7 gives 7x +y +w =28
but y+w=0
therefore 7x=28
x=28/7=4
plugging value of x in eqn.7 we get 16+w=15
w=15-16 =-1
but y+w =0
so y =-w =-(-1) =1
using eqn.8 we get by plugging value of y in it
2+z =4
z=4-2 =2
the answers are x=4, y=1, z=2 and w=-1.
you can check the answer by plugging the values in any equation.
good luck !!!