Question 159560
I'll do the first one to get you started


# 1


"The sum of two numbers is seven" translates to {{{x+y=7}}}



"The sum of the squares of the two numbers is twenty nine" translates to {{{x^2+y^2=29}}}



{{{x+y=7}}} Start with the first equation



{{{y=7-x}}} Subtract "x" from both sides



{{{x^2+y^2=29}}} Move onto the second equation



{{{x^2+(7-x)^2=29}}} Plug in {{{y=7-x}}}



{{{x^2+49-14x+x^2=29}}} FOIL



{{{x^2+49-14x+x^2-29=0}}} Subtract 29 from both sides



{{{2x^2-14x+20=0}}} Combine like terms.



{{{2(x^2-7x+10)=0}}} Factor out the GCF 2



{{{2(x-5)(x-2)=0}}} Factor {{{x^2-7x+10}}}



{{{x-5=0}}} or {{{x-2=0}}} Set each value equal to zero



{{{x=5}}} or {{{x=2}}} Solve for "x" in each case.


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{{{y=7-x}}} Go back to the first equation



{{{y=7-5}}} Plug in {{{x=5}}}



{{{y=2}}} Subtract


So one pair of numbers is 5 and 2


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{{{y=7-x}}} Go back to the first equation



{{{y=7-2}}} Plug in {{{x=2}}}



{{{y=5}}} Subtract



So another pair of numbers is 2 and 5



So this means that the two numbers are 5 and 2 (or 2 and 5; the order does not matter)