Graphical Solution of a System of Equations

To solve the system of equations graphically, we need to follow the following steps:

1. Write the equations in the form of y = mx + b.
2. Plot the y-intercept (b) on the y-axis.
3. Use the slope (m) to draw the line through the y-intercept.
4. Find the point of intersection of the two lines to get the solution of the system of equations.

Given System of Equations

x + y = 3

2x + 5y = 12

Plotting the Lines

To plot the lines, we need to first write the equations in the form of y = mx + b.

x + y = 3

y = -x + 3

The y-intercept is 3 and the slope is -1. So we plot the point (0, 3) on the y-axis and use the slope to draw the line.

2x + 5y = 12

5y = -2x + 12

y = (-2/5)x + 12/5

The y-intercept is 12/5 and the slope is -2/5. So we plot the point (0, 12/5) on the y-axis and use the slope to draw the line.

Finding the Point of Intersection

To find the point of intersection, we need to look at where the two lines intersect on the graph.



From the graph, we can see that the two lines intersect at the point (2, 1). Therefore, the solution of the system of equations is x = 2 and y = 1.

Conclusion

The given system of equations x + y = 3 and 2x + 5y = 12 can be solved graphically by plotting the lines and finding their point of intersection. The solution of the system of equations is x = 2 and y = 1.