Understanding the System of Equations
To solve the system of equations graphically, we need to plot both equations on a coordinate plane.
Equations to Plot
1. x + 2y = 5
2. 2x - 3y = -4
Finding Intercepts
- For the first equation (x + 2y = 5):
- x-intercept: Set y = 0
- x + 2(0) = 5 → x = 5 → Point (5, 0)
- y-intercept: Set x = 0
- 0 + 2y = 5 → y = 2.5 → Point (0, 2.5)
- For the second equation (2x - 3y = -4):
- x-intercept: Set y = 0
- 2x - 3(0) = -4 → 2x = -4 → x = -2 → Point (-2, 0)
- y-intercept: Set x = 0
- 2(0) - 3y = -4 → -3y = -4 → y = 4/3 → Point (0, 4/3)
Graphing the Lines
- Plot the points for both equations on a graph.
- First equation line: Connect the points (5, 0) and (0, 2.5).
- Second equation line: Connect the points (-2, 0) and (0, 4/3).
Finding the Intersection Point
- The solution to the system of equations is found at the intersection of the two lines.
- Identify the coordinates where the two lines cross. This point represents the values of x and y that satisfy both equations.
Conclusion
By graphing both equations and finding their intersection, you can visually determine the solution to the system of equations. This method aids in understanding the relationship between the equations and their graphical representation.