Help with algebra 1 please 10 points.?

Question

1. y = x + 2 and y = 3 - x. How many solutions exist for this system?

one solution
no solution
infinitely many solutions
cannot be determined

Answer 1

y=x+2---------------->(1)

y=3-x------------------>(2)

Add equation(1) and (2)

2y=5

Divide each side by 2.

y=5/2.

Substitute y = 5/2 in the equation(1)

5/2=x+2

Subtract 2 from each side.

5/2-2 = x

Rewrite the expression with common denominator.

(5-4)/2=x

1/2=x

Therefore x = 1/2 and y = 5/2

Option A is right choice.