Question

how many solutions are there
x+2y=-4
4x+8y=-16

Answer 1

show me the steps

Answer 2

There are infinitely many solutions to this system of equations because the second equation is a multiple of the first equation. This means that the two equations are essentially the same line, and any point on the line is a solution to the system.

Answer 3

To see why there are infinitely many solutions, we can start by simplifying both equations:

1) x + 2y = -4
2) 4x + 8y = -16

If we divide the second equation by 4, we get:
4x/4 + 8y/4 = -16/4
x + 2y = -4

Now we see that the second equation is just a multiple of the first equation. This means that any point (x, y) that satisfies the first equation will also satisfy the second equation, and vice versa. In other words, there are infinitely many solutions because the two equations represent the same line.