-x+4y=4
x-4y=-4
the system has no solution
the system has a unique solution:
the system has infinitely many solutions they must satisfy the following equation:
y=0
the answer is the system has many solutions i just don't know the answer to the equation y=?
I answered this below.
To determine the solution to the system of equations, let's solve the given equations:
1) -x + 4y = 4
2) x - 4y = -4
To eliminate the x-term, we can add equation 1 and equation 2 as follows:
(-x + 4y) + (x - 4y) = 4 + (-4)
-5y = 0
Dividing both sides of the equation by -5 gives us:
y = 0
This means that for any value of x, y must be equal to 0 for the system of equations to be true. Therefore, the system has infinitely many solutions and the equation y = 0 represents one possible solution.
To determine whether the system of equations has a solution, no solution, or infinitely many solutions, we can use the method of solving simultaneous equations, such as substitution or elimination.
Let's solve the given system of equations:
1. -x + 4y = 4 ----(Equation 1)
2. x - 4y = -4 ----(Equation 2)
We can solve this system of equations using the method of substitution.
From Equation 2, we can express x in terms of y:
x = 4y - 4
Substituting this value of x into Equation 1, we get:
-(4y - 4) + 4y = 4
-4y + 4 + 4y = 4
0 = 4
We can see that the equation 0 = 4 is not true, which means there is no solution that satisfies both equations. Thus, the system has no solution.
Regarding the statement about the system having a unique solution or infinitely many solutions, it seems to be incorrect based on the calculations above. The system has no solution. Therefore, there is no answer to the equation y = ?.