Question 1048839

{{{40x+35y=20000}}}....eq.1 

{{{70x+90y=40000}}}.....eq.2
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start with
{{{40x+35y=20000}}}....eq.1 ....solve for {{{x}}}

{{{40x=20000-35y}}}

{{{x=20000/40-35y/40}}}

{{{x=500-(35/40)y}}}........substitute in eq.2



{{{70(500-(35/40)y)+90y=40000}}}......solve for {{{y}}}


{{{35000-((35*70)/40)y+90y=40000}}}

{{{35000-((7*70)/8)y+90y=40000}}}

{{{35000-(490/8)y+90y=40000}}}

{{{90y-(490/8)y=40000-35000}}}

{{{(720/8)y-(490/8)y=5000}}}

{{{(230/8)y=5000}}}

{{{y=5000/(230/8)}}}

{{{y=40000/230}}}


{{{highlight(y=4000/23)}}}

now find {{{x}}}


{{{x=500-(35/40)(4000/23)}}}


{{{x=500-(35*4000)/(40*23)}}}

{{{x=500-(35*100)/23}}}

{{{x=(500*23)/23-3500/23}}}

{{{x=11500/23-3500/23}}}

{{{x=(11500-3500)/23}}}

{{{highlight(x=8000/23)}}}


so, exact solutions are: {{{x = 8000/23}}}, {{{y = 4000/23}}}