Solve the system by graphing. (If the system is inconsistent, enter INCONSISTENT. If the system is dependent, enter DEPENDENT.)
{x-y=4
{2x+3y=13
How can I tell if it is Inconsistent or Dependent
Thank you
http://www.wolframalpha.com/input/?i=plot+x-y%3D4+%2C+2x%2B3y%3D13+
To determine if a system of equations is inconsistent or dependent by graphing, follow these steps:
Step 1: Graph each equation on the same coordinate plane.
For the first equation, y = x - 4, you can start by drawing a straight line that passes through the point (0, -4) and has a slope of 1 (since the coefficient of x is 1).
For the second equation, 2x + 3y = 13, you need to rearrange it to solve for y: y = (13 - 2x)/3. This equation represents a straight line with a slope of -2/3 and a y-intercept of 13/3.
Step 2: Observe the graphed lines and determine the relationship between them.
If the lines intersect at a single point, then the system has a unique solution, and it is not inconsistent or dependent.
If the lines are parallel and do not intersect, then the system is inconsistent, meaning there is no solution that satisfies both equations simultaneously.
If the lines overlap each other, forming the same line, then the system is dependent, meaning there are infinitely many solutions.
So, after graphing the two equations, observe the lines' behavior to determine if they intersect (unique solution), are parallel (inconsistent), or overlap (dependent).
If the lines intersect at a single point, then the system has a unique solution.
If the lines are parallel and do not intersect, then the system is inconsistent.
If the lines overlap each other, forming the same line, then the system is dependent.
By following these steps, you should be able to determine whether your system is inconsistent, dependent, or has a unique solution.