Question 1191180

{{{x + y + z =6}}}........1)
{{{x+2y+3z=10}}}.......2)
{{{x+2y+az=b}}}.........3)
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{{{x + y + z =6}}}........1)
{{{x+2y+3z=10}}}.......2)
____________________________subtract

{{{x+2y+3z-x - y - z =10-6}}}
{{{y+2z  =4}}}.......solve for {{{y}}}
{{{y  =4-2z}}}............1.1)


{{{x + y + z =6}}}........1).........substitute {{{y}}}
{{{x + 4-2z + z =6}}}.....solve for {{{x}}}
{{{x + 4-z  =6}}}
{{{x =z-4+6}}}
{{{x =z+2}}}...............1.2)



{{{x+2y+az=b}}}.........3)........substitute {{{x}}}, {{{y}}}, 

{{{z+2+2(4-2z)+az=b}}}.....solve for {{{z}}}

{{{z+2+8-4z+az=b}}}
{{{z+10-4z+az=b}}}
{{{az-3z=b-10}}}
{{{(a-3)z=b-10}}}
{{{z=(b-10)/(a-3)}}}...........1.3)



then

{{{x =(b-10)/(a-3)+2}}}...............1.2)

and

{{{y  =4-2((b-10)/(a-3))}}}............1.1)



The solutions to the system of equations are: 


{{{x=(b-10)/(a-3)+2}}}

{{{y=4-(2(b-10)/(a-3)) }}}

{{{z=(b-10)/(a-3)}}}  where{{{ a<>3}}}