Determine the number of solutions of this system of linear equations
x + 2y = -4
4x + 8y = -16
To determine the number of solutions of this system of linear equations, we first need to determine if the equations are dependent or independent.
We can see that the second equation is a multiple of the first equation (multiplied by 4), which means that the two equations represent the same line. Therefore, the equations are dependent.
To check for the number of solutions, we can simplify the system of equations by dividing the second equation by 4 to get it in the same form as the first equation:
x + 2y = -4
x + 2y = -4
Now we can see that the two equations are identical. This means that there are infinitely many solutions to this system of equations, as they represent the same line.