Answer:
g(x) = (1/2)x + 3
f(x) = g(x) at (-1/2 , 13/4)
Step-by-step explanation:
g(x) and f(x) will have exactly one solution when they are not parallel (same slope) and when they are not equivalent functions (like doubling or halving all terms).
f(x) = (-5/2)x - 3
g(x) = (1/2)x + 3 <= choose an easy equation.
To find the solution, equate the two functions:
f(x) = g(x)
(-5/2)x - 3 = (1/2)x + 3
(-5/2)x - (1/2)x = 3 + 3 <= move variables to one side, constants to other
(-6/2)x = 6 <= simplify
x = 6 / (-6/2) <=isolate x
x = -6/12
x = -1/2
Substitute x = -1/2 into any equation to find y
g(x) = (1/2)x + 3
g(1/2) = (1/2)(1/2) + 3
g(1/2) = (1/4) + 3
g(1/2) = (1/4) + (12/4) <= find common denominator to add
y = (13/4) <= the function symbol can be replaced by y
The coordinates are (-1/2 , 13/4).
