How many solutions does this system have? Show your work to prove your answer.

x – 2y = 2
y = –2x + 5

1 answer

To find the number of solutions to the system, we can solve the system of equations:

1) x – 2y = 2
2) y = –2x + 5

We can start by substituting equation 2) into equation 1):

x – 2(-2x + 5) = 2
x + 4x - 10 = 2
5x - 10 = 2
5x = 12
x = 12/5

Now we can substitute this value of x into equation 2) to solve for y:

y = -2(12/5) + 5
y = -24/5 + 25/5
y = 1/5

Therefore, the system has a unique solution, since there is only one set of values (12/5, 1/5) that satisfies both equations.