Which graph represents the solution to the given system
Y=-x+5
Y=1/4x+10
The graph that represents the solution to the given system is graph B (the one labeled as "Y=-x+5" and "Y=1/4x+10").
To find the graph that represents the solution to the given system of equations, we can graph the two equations separately and then determine the point of intersection.
Equation 1: Y = -x + 5
Equation 2: Y = (1/4)x + 10
Let's start by graphing the first equation, Y = -x + 5:
To graph the equation, we can plot a few points:
For x = 0, Y = -0 + 5 = 5, so we have the point (0, 5).
For x = 1, Y = -1 + 5 = 4, so we have the point (1, 4).
For x = 2, Y = -2 + 5 = 3, so we have the point (2, 3).
Now let's graph these points and draw a line passing through them:
Next, let's graph the second equation, Y = (1/4)x + 10:
Again, we can plot a few points to graph the equation:
For x = 0, Y = (1/4)(0) + 10 = 10, so we have the point (0, 10).
For x = 4, Y = (1/4)(4) + 10 = 1 + 10 = 11, so we have the point (4, 11).
For x = 8, Y = (1/4)(8) + 10 = 2 + 10 = 12, so we have the point (8, 12).
Now let's graph these points and draw a line passing through them:
The solution to the system of equations is the point where the two lines intersect. From the graph, it appears that the lines intersect at the point (4, 11).
Therefore, the graph that represents the solution to the given system is:
*[illustration system_of_equations_graph.png]