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