Final answer:
The system of linear equations is solved by graphing both lines and finding their intersection point. After graphing, it's found that the lines intersect at point (1, 6), which means the correct answer is option A.
Step-by-step explanation:
Graphical Solution to the System of Linear Equations
To solve the given system of linear equations by graphing, we start by graphing each equation on the same set of axes and identifying their point of intersection. The given equations are:
The solution to the system is the point that satisfies both equations simultaneously, which is where the lines intersect on the graph. We can either graph these equations manually on a paper or use graphing software.
For the first equation y = 2x + 4, the y-intercept is 4 and the slope is 2. This means it crosses the y-axis at (0, 4) and rises 2 units for every 1 unit it moves to the right.
For the second equation y = -x + 7, the y-intercept is 7 and the slope is -1. This means it crosses the y-axis at (0, 7) and falls 1 unit for every 1 unit it moves to the right.
When graphed, these lines will intersect at a certain point. By examining the graph, or by setting the two equations equal to each other:
2x + 4 = -x + 7
and solving for x, we find that x = 1. Substituting x = 1 into either equation to find y, we get y = 6. Thus, the solution to the system is the point (1, 6), and the correct answer is option A).