If (x= , y= , z= ) is the solution, for the system of equations ( aligned 2 x-y+8 z & =13 3 x+4 y+5 z & =18 5 x-2 y+7 z & =20 aligned ) then ( + + = )

Step-by-step solution

According to Cramer's rule, ( aligned & x= = ₁ , y= = ₂ and z= = ₃ & where aligned & = | array ccc 2 & -1 & 8 3 & 4 & 5 5 & -2 & 7 array | & =2(28+10)+1(21-25)+8(-6-20) & =76-4-208=76-212=-136 aligned aligned ) ( aligned ₁ & = | array ccc 13 & -1 & 8 18 & 4 & 5 20 & -2 & 7 array | & =13(28+10)+1(126-100)+8(-36-80) & =(13 38)+26-(8 116) & =494+26-928=-408 ₂ & = | array lll 2 & 13 & 8 3 & 18 & 5 5 & 20 & 7 array | & =2(126-100)-13(21-25)+8(60-90) & =(2 26)+(13 4)-(8 30) & =52+52-240=-136 ₃ & = | array ccc 2 & -1 & 13