Question 1176414

{{{6ax + 7y = 23}}}
{{{ax + 3y =2}}}
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start with

{{{6ax + 7y = 23}}} .........solve for {{{y}}}

{{{7y = 23 -6ax }}}

{{{y = 23/7 -(6ax)/7}}}.......1)

go to

{{{ax + 3y = 2}}}......solve for {{{y}}}
 
{{{3y = 2-ax}}}
  
{{{y = 2/3-(ax)/3}}}.......2)


from  1) and 2) we have

{{{ 23/7 -(6ax)/7 =2/3-(ax)/3}}}

{{{23/7 -2/3= 6ax/7-ax/3}}}...........multiply by {{{21}}}

{{{69-14 =18ax-7ax }}}

{{{55 =11ax }}}

{{{x=55/11a}}}

{{{x=5/a}}}


{{{y = 2/3-(ax)/3}}}..........substitute {{{x}}}

{{{y = 2/3-(a(5/a))/3}}}

{{{y = 2/3-5/3}}}

{{{y = -3/3}}}

{{{y = -1}}}




solution set: ({{{5/a}}},{{{ -1}}}) where {{{a<>0}}}