Question

Solve the pair of linear equations $4x - 5y = 20$ and $3x + 5y = 15$ using the graphical method.

Hint:

For graphical method:
Find two points for each line.
Plot and draw lines.
Intersection point = solution.
If lines intersect at one point → unique solution.

Answer 1

Concept: In the graphical method: 
Each linear equation represents a straight line. 
The solution is the point of intersection of the two lines. 
Step 1: Convert equations into convenient form Equation (1): \[ 4x - 5y = 20 \] Find intercepts: 
If $x = 0$, then $-5y = 20 \Rightarrow y = -4$ 
If $y = 0$, then $4x = 20 \Rightarrow x = 5$ 
So points: $(0, -4)$ and $(5, 0)$ 
Equation (2): \[ 3x + 5y = 15 \] Find intercepts: 
If $x = 0$, then $5y = 15 \Rightarrow y = 3$ 
If $y = 0$, then $3x = 15 \Rightarrow x = 5$ 
So points: $(0, 3)$ and $(5, 0)$ 
Step 2: Graph the lines Plot both pairs of points and draw the lines. 
Step 3: Identify intersection point Both lines intersect at: \[ (5, 0) \] Conclusion: The graphical solution of the equations is: \[ \boxed{(5, 0)} \]