Final answer:
To solve the system of equations, graph each equation and find their point of intersection. The solution is the coordinates of the point where the lines intersect.
Step-by-step explanation:
To graph the system of equations, we need to plot the linear equations and find the point of intersection, which represents the solution. The given equations are y = -x + 3 and 2x + y = 6. To plot the first equation, we can start by finding a few points that satisfy it. For example, when x = 0, y = 3. When x = 1, y = 2, and so on. Plotting these points, we can draw a straight line. Similarly, for the second equation, we can choose x and y values that satisfy it and plot them, resulting in another straight line. The point of intersection of these two lines is the solution to the system of equations.
The solution to the system of equations y = -x + 3 and 2x + y = 6 is the point of intersection between the two lines. By graphing the equations, we find that the lines intersect at the point (2, 1). Therefore, the solution to the system is x = 2 and y = 1.
Learn more about Graphing a system of linear equations