How many solutions do the following equations have?
-x+2y=5
2x-4y=-8
the answer is no Solutions. Show your work on why it doesnt have any solutions
To determine if the system of equations has a solution, we can solve them simultaneously by either substitution or elimination.
Given equations:
1. -x + 2y = 5
2. 2x - 4y = -8
Let's simplify the second equation by dividing it by 2:
2x/2 - 4y/2 = -8/2
x - 2y = -4
Now, let's compare the simplified second equation with the first equation:
-x + 2y = 5
We can see that the coefficients of x and y do not match in the two equations, i.e., -1 is not equal to 1 and 2 is not equal to -2. Therefore, there is no common solution that satisfies both equations simultaneously.
Hence, the system of equations has no solution.