8x-5y=-35
5y-8x=35
Is the above a point, have no solution, or infinatley many solutions?
rearrange things a bit and it's clear the equations are the same.
So, what does that mean?
That would mean that there is no solution because they are the same, they would be consistent, and they would be independent?
To determine whether the given system of equations has a unique solution, no solution, or infinitely many solutions, we can start by simplifying the equations.
The given system of equations is:
8x - 5y = -35 ...(1)
5y - 8x = 35 ...(2)
To determine the solution, we can rearrange equation (2) to solve for y:
5y = 8x + 35
y = (8x + 35)/5
Now, let's compare the slopes of the two equations. The slope-intercept form of an equation is y = mx + b, where m represents the slope.
The slope of equation (1) is 8/5, and the slope of equation (2) is -8/5.
Since the slopes of the two equations are not equal (one is positive and the other is negative), this means the lines represented by the two equations are not parallel.
Therefore, the given system of equations represents two lines that intersect at a single point. This implies that the system has a unique solution.
In summary, the given system of equations has a unique solution, which is a single point of intersection between the two lines.