Solve the following system of equations graphically on the set of axes below.
y, equals, minus, x, plus, 2
y=−x+2
y, equals, start fraction, 3, divided by, 5, end fraction, x, minus, 6
y=
5
3
x−6
Since the equations are already in slope-intercept form (y = mx + b), we can easily graph them.
First, let's graph y = -x + 2:
- Plot the y-intercept at b = 2
- Use the slope of -1 to find another point (rise -1, run 1)
- Connect the points with a line
Next, let's graph y = (3/5)x - 6:
- Plot the y-intercept at b = -6
- Use the slope of 3/5 to find another point (rise 3, run 5)
- Connect the points with a line
Now, let's analyze the intersection point of the two lines if it exists. If there is no intersection point, then the system of equations does not have a solution.
The intersection point is where the two lines intersect each other. It represents the solution to the system of equations.
Once you have graphed the two lines, determine where they intersect. That point will be the solution to the system of equations.
Without being able to graph it for you, it seems that the intersection point should be around (4, -2).