Solve the following system of equations graphically on the set of axes below.
Y= 1/2x+1
Y=-3x-6
To graphically solve the system of equations, we need to plot the two lines on the same set of axes.
First, let's graph the line represented by the equation Y = (1/2)x + 1:
- Pick two points on the line. Plug in x = 0, and x = 2, to find the corresponding y-values.
For x = 0, y = (1/2)(0) + 1 = 1.
For x = 2, y = (1/2)(2) + 1 = 2 + 1 = 3.
- Plot the two points: (0, 1) and (2, 3).
- Draw a straight line passing through the two points.
Next, let's graph the line represented by the equation Y = -3x - 6:
- Pick two points on the line. Plug in x = 0, and x = 2, to find the corresponding y-values.
For x = 0, y = -3(0) - 6 = -6.
For x = 2, y = -3(2) - 6 = -6 - 6 = -12.
- Plot the two points: (0, -6) and (2, -12).
- Draw a straight line passing through the two points.
Now, we have both lines graphed on the same set of axes. The solution to the system of equations is the point where the two lines intersect.
It appears that the two lines intersect near (-4, -8).
Here is a visual representation of the graph:
(See attached image)