How many solutions does this system have? x−2y=2y=−2x+5 (1 point) Responses infinitely many solutions infinitely many solutions no solutions no solutions two solutions two solutions one solution
The given system of equations is x - 2y = 2 and y = -2x + 5.
We can start by solving one equation for one variable and substituting it into the other equation.
From the second equation, we can express y in terms of x as y = -2x + 5.
Now we can substitute this expression for y in the first equation:
x - 2(-2x + 5) = 2
Expanding and simplifying:
x + 4x - 10 = 2
Combining like terms:
5x - 10 = 2
Adding 10 to both sides:
5x = 12
Dividing both sides by 5:
x = 12/5
Now we can substitute this value of x back into the second equation to find y:
y = -2(12/5) + 5
Simplifying:
y = -24/5 + 25/5
y = 1/5
So the system has one solution, (x, y) = (12/5, 1/5).
The correct answer is: one solution.