How many solutions does this system have?

x-2y=2
y=-2x+5

a. infinitely many solutions
b. no solutions***
c. two solutions
d. one solution

To determine the number of solutions for a system of equations, we can solve the equations and observe their relationship.

Let's solve this system algebraically using the method of substitution:

Given equations:
1) x - 2y = 2      Equation (1)
2) y = -2x + 5   Equation (2)

We'll begin by solving Equation (2) for y:
y = -2x + 5

Now substitute the value of y in Equation (1) with (-2x + 5):
x - 2(-2x + 5) = 2

Simplify the equation by distributing the negative sign:
x + 4x - 10 = 2

Combine like terms:
5x - 10 = 2

Add 10 to both sides of the equation:
5x = 12

Divide both sides by 5 to solve for x:
x = 12/5

Now substitute the value of x in Equation (2):
y = -2(12/5) + 5
y = -24/5 + 25/5
y = 1/5

So, the solution for this system of equations is x = 12/5 and y = 1/5.

Now, to determine the number of solutions:
Since we obtained a unique solution for x and y, which are (12/5, 1/5), the answer is option d. one solution.

wrong.

no solutoion

ifinitely many solutions

its total legit chestnut

The correct answer is D one solution.