Graphical Representation of Equations 3x + 5y = 8 and 6x + 10y = 4

Plotting the Equations:
- To graph the equations 3x + 5y = 8 and 6x + 10y = 4, we need to first convert them into slope-intercept form (y = mx + b).
- For the equation 3x + 5y = 8:
- 5y = -3x + 8
- y = (-3/5)x + 8/5
- For the equation 6x + 10y = 4:
- 10y = -6x + 4
- y = (-6/10)x + 4/10
- y = (-3/5)x + 2/5

Plotting the Lines:
- Plotting the lines on a graph will give us the intersection point, which is the solution to the system of equations.
- The first line (3x + 5y = 8) has a slope of -3/5 and a y-intercept of 8/5.
- The second line (6x + 10y = 4) has the same slope as the first line but a different y-intercept of 2/5.

Intersecting Point:
- The lines intersect at a single point, which is the solution to the system of equations.
- By plotting the lines and finding the intersection point, we can determine the values of x and y that satisfy both equations simultaneously.

Conclusion:
- Graphing the equations 3x + 5y = 8 and 6x + 10y = 4 allows us to visually see where the lines intersect, providing us with the solution to the system of equations.