If the system of equations aligned & 2 x-y+z=4 & 5 x+ y+3 z=12 & 100 x-47 y+ z=212 aligned has infinitely many solutions, then -2 is equal to

Step-by-step solution

aligned & 2 x-y+z=4 & 5 x+ y+3 z=12 & 100 x-47 y+ z=212 & x= y= z=0 & z= | array ccc 2 & -1 & 4 5 & & 12 100 & -47 & 212 array |=0 & 2(212 +564)+1(1060-1200) & 424 +1128-140-940-400 =0 & =-2 & y= | array ccc 2 & -1 & 1 5 & -2 & 3 100 & -47 & array |=0 & 2(-2 +141)+1(5 -300)+1(-235+200)=0 & =53 & -2 =53-2(-2)=57 aligned