two systems of equations are giving below for each system choosethe best description of its solution if applicable give solution
x+4y=8
-x-4y= -8
choose which one this problem fit in
1)the system has no solution
2) the system has a unique solution (x,y)=
or the system has a infinitely many solutions they must satisfy the following equation: y=
To determine the solution of this system of equations, we can solve it using the method of elimination. The goal is to eliminate one of the variables, either x or y, by adding or subtracting the two equations. Let's proceed:
Adding the two equations together, we get:
(x + 4y) + (-x - 4y) = 8 + (-8)
This simplifies to:
0 = 0
As a result, we end up with 0 = 0, which is a true statement. This means that the two equations are dependent and represent the same line. Therefore, they have infinitely many solutions. Any values of x and y that satisfy the equation y = can be considered as solutions.
In conclusion, the system of equations provided has infinitely many solutions, and the solutions must satisfy the equation y = .
for some reason when I am adding the two equations, I am getting 0 = 0. This is a true statement which means that there is an infinite number of solutions. Any x,y pair that works in one will work in the other.
x = 8 - 4y
8 - 4y - 4y = -8
-8y = -16
y = 2
-x-4y= -8
-x -8 = -8