Final answer:
To find the coordinates of each corner point for a given system of inequalities, plot the lines on a graph and identify the intersection points. Solve for the x and y values of each intersection point.
Step-by-step explanation:
To find the coordinates of each corner point for the given system of inequalities, we can solve the system of equations by graphing them. Start by plotting the lines x+4y=34, 5x+y=37, and 6x+5y=52 on a coordinate plane.
The points where the lines intersect are the corner points. Find the x and y values of each intersection point to determine the coordinates.
For example, let's solve for the intersection point of the first two lines:
Convert the equations to slope-intercept form: y = (-1/4)x + 8.5 and y = -5x + 37.
Graph the lines on a coordinate plane.
The point where the lines intersect is the solution. Based on the graph, the intersection point is (18.6, 5).
Similarly, solve for the intersection points of the other lines to get the coordinates of the remaining corner points.