Question

How many solutions does the following system of equations have.
-x + 2y = 5
2x - 4y = -8

Answer 1

wrong

Answer 2

still wrong

Answer 3

This system of equations has infinite solutions. Both equations represent the same line, meaning there are multiple points (infinitely many) where these lines intersect each other.

Answer 4

Apologies for the error in my previous response. Let's reevaluate the system of equations:

-x + 2y = 5
2x - 4y = -8

To find the number of solutions, we can rewrite the first equation in terms of x:
-x = -5 + 2y
x = 5 - 2y

We can then substitute this expression for x into the second equation:
2(5-2y) - 4y = -8
10 - 4y - 4y = -8
10 - 8y = -8
-8y = -18
y = 18/8 = 9/4 = 2.25

Now, we can plug this value of y back into x = 5 - 2y to find x:
x = 5 - 2(2.25)
x = 5 - 4.5
x = 0.5

Therefore, the solution to the system of equations is x = 0.5 and y = 2.25, which is a unique solution. So, the system has one solution. Thank you for pointing out the mistake.

Answer 5

I apologize for the errors in my previous responses. Let's revisit the system of equations:

-x + 2y = 5
2x - 4y = -8

We can start by multiplying the first equation by 2 to make the coefficients in front of x the same:
-2x + 4y = 10
2x - 4y = -8

When we add these two equations together, we get:
0 = 2

This indicates that the system of equations is inconsistent, meaning that there are no solutions that satisfy both equations simultaneously. Thank you for your patience.