Question

According to projections through the year​ 2030, the population y of the given state in year x is approximated by

State​ A:
−6x+y=11,200
State​ B:
−135x+y=9,000
where x=0 corresponds to the year 2000 and y is in thousands. In what year do the two states have the same​ population?

The two states will have the same population in the year:

Answer 1

In what year do the two states have the same​ population?
or in other words

what is "x" when both "y"'s are equal?

`-6x+y=11200\implies \hspace{5.8em} y=11200+6x \\\\\\ -135x+y=9000\implies\hspace{5em} y=9000+135x \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{when both of them are equal} }{11200+6x~~ = ~~9000+135x}\implies 2200+6x=135x\implies 2200=129x \\\\\\ \cfrac{2200}{129}=x\implies 17.05\approx x\hspace{5em}\approx \stackrel{ \textit{x=0 to }x\approx 17 }{\text{\LARGE 2017}}`