Question 1203153


 {{{ 3a - 12b - 2c = 5}}}.....eq.1
{{{ 4a - 3b + 8c = 5}}}.......eq.2
{{{ 6a + 9b + 16c = 4}}}......eq.3
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 {{{ 3a - 12b - 2c = 5}}}.....eq.1.....multiply by {{{2}}}
{{{ 6a + 9b + 16c = 4}}}......eq.3
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{{{ 6a - 24b - 4c = 10}}}
{{{ 6a + 9b + 16c = 4}}}
-----------------------------------subtract

{{{ 6a - 24b - 4c -(6a + 9b + 16c )= 10-4}}}

{{{ 6a - 24b - 4c -6a - 9b - 16c = 6}}}

 {{{ - 33b   - 20c = 6}}}...solve for {{{b}}}

{{{ - 6   -  33b=20c}}} 

{{{ c=- 6/20   - 33b/20}}}.........eq.1a



{{{  3a - 12b - 2c = 5}}}.....eq.1
{{{ 4a - 3b + 8c = 5}}}.......eq.2.....multiply by {{{4}}}
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{{{ 3a - 12b - 2c = 5}}}
{{{ 16a - 12b + 32c = 20}}}
-----------------------------------subtract

{{{ 3a - 12b - 2c-(16a - 12b + 32c) = 5-20}}}

{{{ 3a - 12b - 2c-16a + 12b -32c= -15}}}

{{{ -13a  -34c= -15}}}....multiply by {{{-1}}}

{{{ 13a  +34c= 15}}}.............solve for {{{c}}}

{{{ c= 15/34-13a/34}}}........eq.1b


from eq.1a and eq.1b we have


{{{ - 6/20   - 33b/20=15/34-13a/34}}}...........solve for {{{b}}}

{{{ b = 130a/561 - 84/187}}}......eq.1c


go to eq.1, substitute {{{b}}} and {{{c}}}


 {{{ 3a - 12(130a/561 - 84/187) - 2(15/34-13a/34) = 5}}}.....eq.1.... solve for {{{a}}}

 {{{ 3a - 520a/187 + 1008/187 +13a/17 - 15/17= 5}}}

{{{ 3a - 520a/187   +13a/17 = 5-1008/187+ 15/17}}}

{{{ 3a - 520a/187   +13a/17 = 5-1008/187+ 15/17}}}

{{{ 184a/187=92/187}}}

{{{ 184a=92}}}

{{{ a=92/184}}}

{{{ a=1/2}}}


go to


{{{ b = 130a/561 - 84/187}}}......eq.1c, substitute {{{a}}}

{{{ b = 130(1/2)/561 - 84/187}}}

{{{ b = -1/3}}}


go to


{{{ c= 15/34-13a/34}}}........eq.1b, substitute {{{a}}}

{{{ c= 15/34-13(1/2)/34}}}

{{{ c= 1/4}}}

solution:

{{{ a=1/2}}}

{{{ b=-1/3}}}

{{{ c=1/4}}}