Question 199077
Let x=Amount he invested at 7% and y=Amount he invested at 4%


Since he has a total of $10,000, this means that {{{x+y=10000}}}


Also, since he invested some at 7% and the rest at 4%, and received $640, this tells us that {{{0.07x+0.04y=640}}}



{{{7x+4y=64000}}} Multiply both sides by 100 to make every number whole.




So we have the system of equations:



{{{system(x+y=10000,7x+4y=64000)}}}



{{{-7(x+y)=-7(10000)}}} Multiply the both sides of the first equation by -7.



{{{-7x-7y=-70000}}} Distribute and multiply.



So we have the new system of equations:

{{{system(-7x-7y=-70000,7x+4y=64000)}}}



Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:



{{{(-7x-7y)+(7x+4y)=(-70000)+(64000)}}}



{{{(-7x+7x)+(-7y+4y)=-70000+64000}}} Group like terms.



{{{0x+-3y=-6000}}} Combine like terms.



{{{-3y=-6000}}} Simplify.



{{{y=(-6000)/(-3)}}} Divide both sides by {{{-3}}} to isolate {{{y}}}.



{{{y=2000}}} Reduce.



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{{{-7x-7y=-70000}}} Now go back to the first equation.



{{{-7x-7(2000)=-70000}}} Plug in {{{y=2000}}}.



{{{-7x-14000=-70000}}} Multiply.



{{{-7x=-70000+14000}}} Add {{{14000}}} to both sides.



{{{-7x=-56000}}} Combine like terms on the right side.



{{{x=(-56000)/(-7)}}} Divide both sides by {{{-7}}} to isolate {{{x}}}.



{{{x=8000}}} Reduce.



So the solutions are {{{x=8000}}} and {{{y=2000}}}.



This means that he invested $8,000 at 7% and $2,000 at 4%