How many solutions does the following system of equations have? −𝑥 + 2𝑦 = 5 2𝑥 − 4𝑦 = −8 S. One Solution T. No Solutions U. Infinite Solution

Answer 1

S. One Solution

Answer 2

wrong

Answer 3

T. No Solutions

Answer 4

explain

Answer 5

By examining the two equations, we can see that they are actually multiples of each other:

-𝑥 + 2𝑦 = 5

2𝑥 − 4𝑦 = −8

If we multiply the first equation by 2, we get:

-2𝑥 + 4𝑦 = 10

Comparing the second equation with this new equation, we see that they are equivalent. This means that the two original equations represent the same line in the xy-plane. When two equations represent the same line, there are infinitely many solutions, because any point on that line would satisfy both equations. Therefore, the system of equations has infinitely many solutions.