Solve Problems Using Systems of Linear Equations
-In the Town $x$

Solve Problems Using Systems of Linear Equations
-In the town of Milton Lake, the percentage of women who smoke is increasing while the percentage of men who smoke is decreasing.
Let $x$ represent the number of years since 1990 and y represent the percentage of women in Milton Lake who smoke. The graph of $y$ against $x$ includes the data points $( 0,16.4 )$ and $( 14,20.32 )$ . Let $x$ represent the number of years since 1990 and y represent the percentage of men in Milton Lake who smoke. The graph of $y$ against $x$ includes the data points $( 0,28.3 )$ and $( 10,26.2 )$ .
Determine when the percentage of women who smoke will be the same as the percentage of men who smoke. Round to the nearest year. What percentage of women and what percentage of men (to the nearest whole percent) will smoke at that time?
[Hint: first find the slope-intercept equation of the line that models the percentage, $\mathrm { y }$ , of women who smoke x years after 1990 and the slope-intercept equation of the line that models the percentage, $y$ , of men who smoke x years after 1990]

A) $2014 ; 23 \%$
B) $2018 ; 22 \%$
C) $2012 ; 24 \%$
D) $2016 ; 23 \%$