5x-4y=24
4y-5x=-24
what is the solution of the systme of equations? ( i guess no solution)
is the sytem consistant or inconsistant? (i guess consistant)
is it dependent or independent
(i guess dependen)
To find the solution to the system of equations:
5x - 4y = 24 -----(1)
4y - 5x = -24 -----(2)
We can solve this system of equations by using the method of elimination. The idea is to add or subtract the equations in a way that eliminates one of the variables.
To eliminate variables, let's multiply equation (2) by -1:
-1(4y - 5x) = -1(-24)
-4y + 5x = 24
Now, let's add equation (1) and equation (2) together:
(5x - 4y) + (-4y + 5x) = 24 + 24
5x - 4y - 4y + 5x = 48
10x = 48
Divide both sides of the equation by 10:
x = 48/10
x = 4.8
Now substitute the value of x into either equation (1) or (2). Let's use equation (1):
5(4.8) - 4y = 24
24 - 4y = 24
-4y = 0
y = 0
Therefore, the system of equations has a unique solution, which is x = 4.8 and y = 0.
The system of equations is consistent because it has a solution.
The system of equations is independent because it has a unique solution. If two equations are dependent, they represent the same line and have infinitely many solutions. In this case, the two equations have different slopes and y-intercepts, indicating they are independent.