Find the type of solution to the system of equations by graphing: 4x + y = 8 and x - 3y = 6

Step 1: Rewrite both equations in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

For the first equation, 4x + y = 8, you can rewrite it as y = -4x + 8.

For the second equation, x - 3y = 6, you can rewrite it as y = 1/3x - 2.

Step 2: Graph both equations on the same set of axes.

The first equation, y = -4x + 8, has a slope of -4 and a y-intercept of 8. So, you start at the point (0,8) on the y-axis and then move down 4 units and to the right 1 unit to plot the next point. Continue this pattern to draw the line.

The second equation, y = 1/3x - 2, has a slope of 1/3 and a y-intercept of -2. So, you start at the point (0,-2) on the y-axis and then move up 1 unit and to the right 3 units to plot the next point. Continue this pattern to draw the line.

Step 3: Look for the point(s) where the lines intersect.

If the lines intersect at one point, then there is one solution to the system of equations, and the system is consistent and independent.

If the lines are parallel and do not intersect, then there are no solutions to the system of equations, and the system is inconsistent.

If the lines coincide (i.e., they are the same line), then there are infinitely many solutions to the system of equations, and the system is consistent and dependent.

By graphing the two equations, you can determine which of these is the case.