I am supposed to figure out if these are consistent or inconsistant ,but I am arriving at only one point for my answer, telling me this is constant but dependent am I doing something horribly wrong?
8x-9y=-63
9y-8x=63
One equation can be derived from the other, by multiplying both sides by -1 and rearranging. They are consistent equations, and there is no unique solution. It is the same as having only one equation for two variables.
I think they are independent am I right?And would my answer be no solution or a point, my worksheet specifies for no solution, a point, and many solutions...I marked a point.
They are not independent. There are many (actually, infinite) solutions
To determine if a system of equations is consistent or inconsistent, you need to check if the equations have a common solution or if they contradict each other. In this case, let's solve the system of equations step by step:
Equation 1: 8x - 9y = -63
Equation 2: 9y - 8x = 63
Step 1: Rearrange Equation 2
To make it easier to solve the system, let's rearrange Equation 2 to isolate y:
9y - 8x = 63
9y = 8x + 63
y = (8/9)x + 7
Step 2: Compare the Slopes
When comparing the two equations, notice that both have the same coefficients for x and y but with opposite signs. This means their slopes are equal. In this example, the slope is 8/9 for both equations.
Step 3: Check for Consistency or Inconsistency
Since the slopes are equal and the y-intercepts are different (0 in Equation 1 and 7 in Equation 2), the system of equations represents two parallel lines. This type of system is called an inconsistent or contradictory system.
Explanation:
Inconsistent systems have no common solution since parallel lines never intersect. Therefore, if you are arriving at a single point as the answer, it means you made an error during the solving process. In this case, the system of equations is inconsistent.