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

Answer 1

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.