Final answer:
To find an equation equivalent to the system of equations y=4-x and y=x/2+19/2, set the two equations equal and solve for x, resulting in x=-11. Substituting x=-11 into the first equation provides the y-value of the intersection point, which is y=15. Thus, the point (-11, 15) represents the solution to the system.
Step-by-step explanation:
The objective is to determine which equation is equivalent to the system consisting of equations F: y = 4 - x and G: y = x/2 + 19/2. To find an equivalent equation, we can solve the system by equating the two expressions for y from equations F and G. This would give us a new equation representing the solution to the system where F and G intersect.
Let's set the two expressions for y equal to each other:
4 - x = x/2 + 19/2
Multiplying every term by 2 to eliminate the fractions, we get:
8 - 2x = x + 19
Adding x to both sides and subtracting 19 from both sides gives us:
-x + 8 = 19
Finally, solving for x gives us:
x = -11
Now, substituting x = -11 into the original equation F, we get:
y = 4 - (-11) = 15
Therefore, the solution to the system of equations where F and G intersect is at the point (-11, 15). This point represents an equivalent condition to the system of equations F and G.