Solution:
Pick two pairs: Eliminate the same variable from each system: Step 1: 4x-3y+z=-10 -2(2x+y+3z=0)= -4x-2y-6z=0 Step2: 4x-3y+z=-10 -4x-2y-6z=0 -5y-5z=10 |
Step 3:
Pick another two pairs 2x+y+3z=0 2(-x+2y-5z=17)= -2x+4y-10z=34 2x+y+3z=0 -2x+4y-10z=34 5y-7z=34 Step 4: Solve the system of the two new equations -5y-5z=-10 5y-7z=34 -12z= 24 -12 -12 z=-2 |
Step 5:
Plug z into one of the two-by-two equations -5y-5(-2)=-10 -5y+10=-10 -10 -10 -5y = -20 -5 -5 y = 4 |
Step 6:
Substitute z and y into one of the orginial equations -x+2y-5z=17 -x+2(4)-5(-2)=17 -x+8+10=17 -x+18=17 -18 18 -x = -1 -1 -1 x=1 |