To solve a system of equations graphically, we need to identify the intersection point where the lines representing the equations cross. In this example, we are given two equations in slope-intercept form: y = 2x + 3 and y = x + 4.

Starting with the first equation, y = 2x + 3, we can determine its graph. The y-intercept is at the point (0, 3), and the slope is 2, indicating that for every 1 unit we move to the right (positive x-direction), we move up 2 units (positive y-direction). Plotting this, we can also move down 2 units and to the left 1 unit to find additional points. Connecting these points gives us the line for this equation.

Next, we analyze the second equation, y = x + 4. Here, the y-intercept is at (0, 4), and the slope is 1, meaning we move up 1 unit and over 1 unit to the right. This line can also be plotted similarly, and connecting the points will yield its graph.

To find the intersection point, we look for where these two lines cross. From the graph, we can see that they intersect at the point (1, 5). This point is crucial as it represents the solution to the system of equations.

To verify that (1, 5) is indeed a solution to both equations, we substitute the x and y values into each equation. For the first equation, substituting gives us:

y = 2x + 3

Substituting x = 1 and y = 5:

5 = 2(1) + 3

5 = 2 + 3

5 = 5, which is a true statement.

Now, we check the second equation:

y = x + 4

Substituting x = 1 and y = 5:

5 = 1 + 4

5 = 5, which is also a true statement.

Since both equations yield true statements when substituting the intersection point (1, 5), we conclude that this point is indeed a solution to the system of equations.