The data can be modeled by the following system of linear equations. $K$ \[ \left\{\begin{aligned} -4 x+20 y=140 & \text { Equation 1 } \\ x+3 y=146 & \text { Equation 2 } \end{aligned}\right. \] Equation 1 is modeled for the percentage of never-married American adults, $y, x$ years after 1970 and Equation 2 is modeled for the percentage of married American adults, $y, x$ years after 1970. Use these models to complete parts $a$ and $b$. a. Determine the year, rounded to the nearest year, when the percentage of never-married adults will be the same as the percentage of married adults. For that year, approximately what percentage of Americans, rounded to the nearest percent, will belong to each group? In year $\square$ the percentage of never-married adults will be the same as the percentage of married adults. For that year, approximately $\%$ percentage of Americans will belong to each group.

Step 1 ：We are given two equations that model the percentage of never-married and married American adults, respectively, $x$ years after 1970. The equations are: \(-4x + 20y = 140\) and \(x + 3y = 146\).

Step 2 ：We are asked to find the year when the percentage of never-married adults will be the same as the percentage of married adults. This means we need to find the point where the two equations intersect. This can be done by setting the two equations equal to each other and solving for $x$ and $y$. The $x$ value will represent the year and the $y$ value will represent the percentage.

Step 3 ：Solving the system of equations, we find that $x = \frac{625}{8}$ and $y = \frac{181}{8}$. This means that the year when the percentage of never-married adults will be the same as the percentage of married adults is $\frac{625}{8}$ years after 1970, and the percentage of Americans that will belong to each group is $\frac{181}{8}$ percent.

Step 4 ：However, the question asks for the year and percentage rounded to the nearest year and percent, respectively. Therefore, we need to round these values. Rounding $x$ to the nearest year, we get $x = 78$. Rounding $y$ to the nearest percent, we get $y = 23$.

Step 5 ：Finally, adding the value of $x$ to 1970 to get the actual year, we find that in year \(\boxed{1970 + 78 = 2048}\) the percentage of never-married adults will be the same as the percentage of married adults. For that year, approximately \(\boxed{23\%}\) of Americans will belong to each group.