Question

Determine the number of solutions of this system of linear equations:%0D%0A%0D%0Ax+2y=−4%0D%0A%0D%0A+%0D%0A2%0D%0A%0D%0A=%0D%0A−%0D%0A4%0D%0A%0D%0A4x+8y=−16%0D%0A4%0D%0A%0D%0A+%0D%0A8%0D%0A%0D%0A=%0D%0A−%0D%0A16%0D%0A%0D%0AThis question requires you to show your work.%0D%0A%0D%0A(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

First, let's simplify the system of equations:

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

We see that the second equation is equivalent to the first equation multiplied by 4:

4(x + 2y) = -16

This means that the second equation is redundant and does not provide any new information. The two equations are essentially the same, just multiplied by different constants.

Therefore, this system of equations is considered dependent, and it has infinitely many solutions.