6y-7x=12, 7x-6y=-12
solve by graphing method. classify as consistent/inconsistent and dependent/independent.
i have been working on this problem and i can't figure it out.
please help!
there is no work involved. Graph the lines.
It looks to me to be the same line. Therefore, they are consistent (there is at least one solution), and undetermined (there is an infinite number of solutions), and dependent (there is an infinite number of solutions).
http://www.algebra.com/algebra/homework/coordinate/Types-of-systems-inconsistent-dependent-independent.lesson
**Thank you so much for your help!**
To solve the system of equations using the graphing method, you need to graph both equations on the same coordinate plane and find the point where the two lines intersect. This point represents the solution to the system.
First, let's rearrange the equations in the form "y = mx + b" to make them easier to graph:
Equation 1: 6y - 7x = 12
Solve for y:
6y = 7x + 12
y = (7/6)x + 2
Equation 2: 7x - 6y = -12
Solve for y:
-6y = -7x - 12
y = (7/6)x + 2
Now that we have both equations in slope-intercept form, we can graph them on the same coordinate plane. The slope of both equations is (7/6), which means the lines will be parallel. They will either never intersect and be inconsistent, or they will coincide and be dependent.
Plotting the points on the coordinate plane, you can see that the lines are identical and perfectly overlap each other. This means they have infinitely many solutions and are dependent.
To classify as consistent or inconsistent, we can see that the lines coincide, so they are consistent.
Similarly, to classify as dependent or independent, because the lines coincide perfectly, they are dependent.
Therefore, the system of equations is consistent and dependent.