Solving the Equations using the Graphical Method

To solve the given system of equations, we can use the graphical method. This method involves graphing the equations on a coordinate plane and finding the intersection point, which represents the solution to the system.

Step 1: Convert the Equations to Slope-Intercept Form

To graph the equations, we need to convert them to slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

Given equations:
1) 2x + y = 5
2) 3x + 2y = 8

Converting equation 1 to slope-intercept form:
2x + y = 5
y = -2x + 5

Converting equation 2 to slope-intercept form:
3x + 2y = 8
2y = -3x + 8
y = (-3/2)x + 4

Step 2: Graph the Equations

Now that we have the equations in slope-intercept form, we can graph them on a coordinate plane.

To graph each equation, we can plot a few points and draw a straight line passing through those points.

For equation 1 (y = -2x + 5):
- Plot the y-intercept at (0, 5) --> (0, b) = (0, 5)
- Use the slope (-2) to find another point: move 1 unit to the right and 2 units down from the y-intercept --> (1, 3)
- Draw a straight line passing through the two points.

For equation 2 (y = (-3/2)x + 4):
- Plot the y-intercept at (0, 4) --> (0, b) = (0, 4)
- Use the slope (-3/2) to find another point: move 2 units to the right and 3 units down from the y-intercept --> (2, 1)
- Draw a straight line passing through the two points.

Step 3: Find the Intersection Point

Now that we have graphed both equations, we can find the intersection point by visually inspecting the graph.

The intersection point represents the solution to the system of equations.

Step 4: Analyze the Intersection Point

By analyzing the intersection point, we can determine the solution to the system of equations.

In this case, the intersection point is approximately (2, 1). This means that x = 2 and y = 1.

Therefore, the solution to the given system of equations is x = 2 and y = 1.

Conclusion:

The given system of equations, 2x + y = 5 and 3x + 2y = 8, can be solved using the graphical method. By graphing the equations on a coordinate plane and finding the intersection point, we determined that the solution to the system is x = 2 and y = 1.