5x-4y=24
4y-5x=-24
what is the solution of the systme of equations? ( i guess no solution)
is the sytem consistant or inconsitatn? (i guess con)
is it dependent or independent
(i guess dependen)
There is no solution. The two equations are consistent and dependent. Actually, in spite of their different appearance, they are really the same equation, and both would be graphed as the same line.
I don't know but,I think you're correct.
To solve the system of equations, we can use a method called elimination. Let's go step by step:
1. Start by multiplying the second equation by -1 to change the signs:
-1(4y - 5x) = -1(-24)
-4y + 5x = 24
2. Now, we can add the two equations together to eliminate the variable y:
(5x - 4y) + (-4y + 5x) = 24 + (-24)
5x - 4y - 4y + 5x = 0
3. Simplify the equation:
10x - 8y = 0
4. Divide the entire equation by 2 to simplify it further:
(10x - 8y)/2 = 0/2
5x - 4y = 0
Both equations 5x - 4y = 0 and 5x - 4y = 24 are the same. This indicates that the two equations represent the same line.
Since the equations represent the same line, there is no unique solution to the system of equations. Thus, your initial guess of no solution is correct.
A system of equations is consistent when there is at least one solution to the system. In this case, since there is no unique solution, the system is inconsistent.
Finally, when two equations represent the same line, they are dependent on each other. Therefore, the system of equations is dependent.