The sum of two numbers is 35 and their difference is 5 . What are the two numbers? Let \( x= \) one number and \( y= \) the other number. The corresponding modeling system is \( \left\{\begin{array}{l}x+y=35 \\ x-y=5\end{array}\right. \). Solve the system graphically.
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To solve the system graphically, start by rearranging the equations into slope-intercept form. For the first equation \(x + y = 35\), rearranging gives \(y = -x + 35\). For the second equation \(x - y = 5\), we rearrange to \(y = x - 5\). Next, plot the two lines on a graph. The line \(y = -x + 35\) will have a negative slope, crossing the y-axis at 35, while \(y = x - 5\) has a positive slope and crosses the y-axis at -5. The intersection point of these two lines will give you the values of \(x\) and \(y\). Solving them gives the intersecting point at \(x = 20\) and \(y = 15\). So, the two numbers are 20 and 15! Happy graphing!