Question

Using the replacement set, find the solutions for the equation.
y = 0.5x + 10 Replacement Set: {(-2, 9.5), (0, 10),(3, 11.5),(4, 13)}

Answer 1

(0, 10),(3, 11.5)

Answer 2

I'm not 100% clear on what a replacement set is, never studied it myself. My brief amount of research tells me that the elements in the replacement set are possible solutions of the equation, and you have to determine if they make the cut, so to speak.

For example, take the point (-1, 5), that's (x,y). Try out the value of x, and see if you get the correct y:
\[y=0.5(-1)+10=9.5\]\[9.5\neq5\], therefore (-1, 5) is not a solution (but (-1, 9.5) is for future reference).
Try the point (2, 11), i.e. x=2, y=11:
\[y=0.5(2)+10=11\]\[11=11\], therefore (2,11) is a solution.

Answer 3

"a" is a list of Mathematica, brace delimited, replacement rules.
a = {{x -> -2, y -> 9.5}, {x -> 0, y -> 10}, {x -> 3,
y -> 11.5}, {x -> 4, y -> 13}}

y == 0.5x + 10 /. a yields the following:
{False, True, True, False}

"/." means apply the replacement rules labeled "a"