The sum of two numbers is 30 and their difference is 20 . What are the two numbers? \( \left\{\begin{array}{l}x+y=30 \\ x-y=20\end{array}\right. \). \( x= \) one the system graphically. symber and \( y=t \) the other number. The corresponding modeling

To solve the system of equations, we first can rearrange them. From \( x + y = 30 \), we can express \( y \) in terms of \( x \): \( y = 30 - x \). From \( x - y = 20 \), we can express \( y \) as well: \( y = x - 20 \). By setting these two expressions for \( y \) equal to each other, we get \( 30 - x = x - 20 \). Simplifying this gives us \( 2x = 50 \), leading to \( x = 25 \). Substituting back gives \( y = 30 - 25 = 5 \). So, the two numbers are 25 and 5! Graphically, you could represent these equations on a coordinate plane. Each equation corresponds to a line: the line representing the first equation will intersect the second one at the point (25, 5). This intersection point gives the solution to the system of equations, thus confirming that these two numbers indeed add up to 30 while having a difference of 20.