Graphical Solution of the System of Equations
To solve the system of equations x + y = 3 and 2x - 5y = 12 graphically, we need to plot the two equations on the same coordinate plane and find the point of intersection.

Plotting the First Equation
- For the equation x + y = 3, we rearrange it to y = 3 - x.
- We can start by plotting the y-intercept at (0, 3) and then use the slope of -1 to find another point.
- Connect the two points to draw a line representing the first equation.

Plotting the Second Equation
- For the equation 2x - 5y = 12, we rearrange it to y = (2x - 12)/5.
- We can start by plotting the y-intercept at (0, -2.4) and then use the slope of 2/5 to find another point.
- Connect the two points to draw a line representing the second equation.

Finding the Point of Intersection
- The point where the two lines intersect is the solution to the system of equations.
- By visually inspecting the graph, we can see that the lines intersect at the point (3, 0).
- Therefore, the solution to the system of equations is x = 3 and y = 0.

Conclusion
- By graphically plotting the two equations and finding the point of intersection, we were able to solve the system of equations x + y = 3 and 2x - 5y = 12.
- Graphical method provides a visual representation of the solution and helps in understanding the relationship between the two equations.