Question 375689
Since (2p, 5p-4) is a solution, this means that {{{x=2p}}} and {{{y=5p-4}}}



{{{y=5x+16}}} Start with the given equation.



{{{5p-4=5(2p)+16}}} Plug in {{{x=2p}}} and {{{y=5p-4}}} 



{{{5p-4=10p+16}}} Multiply



{{{5p=10p+16+4}}} Add {{{4}}} to both sides.



{{{5p-10p=16+4}}} Subtract {{{10p}}} from both sides.



{{{-5p=16+4}}} Combine like terms on the left side.



{{{-5p=20}}} Combine like terms on the right side.



{{{p=(20)/(-5)}}} Divide both sides by {{{-5}}} to isolate {{{p}}}.



{{{p=-4}}} Reduce.



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Answer:


So the solution is {{{p=-4}}} 



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