Step 1: Understanding the Question:
We are asked to find the solution \((x, y)\) for a system of two linear equations. The method specified is the graphical method, which means we need to plot the lines corresponding to each equation and find their point of intersection.
Step 2: Key Formula or Approach:
The graphical method involves the following steps:
1. For each equation, find at least two coordinate points \((x, y)\) that lie on the line. The easiest points to find are usually the x-intercept (where \(y=0\)) and the y-intercept (where \(x=0\)).
2. Plot these points on a Cartesian coordinate system and draw a straight line through them for each equation.
3. The coordinates of the point where the two lines intersect is the solution to the system of equations.
Step 3: Detailed Explanation:
Line 1: $4x - 5y = 20$
Find the y-intercept (set \(x=0\)):
\(4(0) - 5y = 20 \Rightarrow -5y = 20 \Rightarrow y = -4\). Point is \((0, -4)\).
Find the x-intercept (set \(y=0\)):
\(4x - 5(0) = 20 \Rightarrow 4x = 20 \Rightarrow x = 5\). Point is \((5, 0)\).
So, the first line passes through \((0, -4)\) and \((5, 0)\).
Line 2: $3x + 5y = 15$
Find the y-intercept (set \(x=0\)):
\(3(0) + 5y = 15 \Rightarrow 5y = 15 \Rightarrow y = 3\). Point is \((0, 3)\).
Find the x-intercept (set \(y=0\)):
\(3x + 5(0) = 15 \Rightarrow 3x = 15 \Rightarrow x = 5\). Point is \((5, 0)\).
So, the second line passes through \((0, 3)\) and \((5, 0)\).
Plotting and Finding Intersection:
When we plot these lines, we notice that the point \((5, 0)\) is on both lines. This means it is the point where the two lines intersect.
Step 4: Final Answer:
The graphical solution to the system of equations is the intersection point \((5, 0)\).
\[
\boxed{(5, 0)}
\]