Final answer:
Upon solving the system of equations, the lengths of EF and FG are found to be 8 and 15 respectively.
Step-by-step explanation:
If EF = 2x - 12, FG = 3x - 15, and EG = 23, to find EF and FG we must first recognize that segment EG is the sum of segments EF and FG since those two segments are consecutive. So we can write the equation 2x - 12 + 3x - 15 = 23. Combining like terms gives us 5x - 27 = 23. We then add 27 to both sides to get 5x = 50. Dividing each side by 5, we get x = 10. We substitute x = 10 back into the expressions for EF and FG to find their lengths:
EF = 2(10) - 12 = 20 - 12 = 8
FG = 3(10) - 15 = 30 - 15 = 15