Final answer:
After substituting the x-value of the point (5/3,-2/3) into both equations, we find that it results in the y-value of -2/3 for each equation. Hence, the point (5/3,-2/3) is a solution to the system of equations.
Step-by-step explanation:
To verify if the point (5/3,-2/3) is a solution to the system of equations y=1/2x-3/2 and y=-x+1, we need to check whether the point satisfies both equations.
For the first equation:
Substitute x = 5/3 into y = 1/2x - 3/2:
y = (1/2)(5/3) - 3/2 = 5/6 - 3/2 = 5/6 - 9/6 = -4/6 = -2/3
For the second equation:
Substitute x = 5/3 into y = -x + 1:
y = -(5/3) + 1 = -5/3 + 3/3 = -2/3
Since the point gives a value of y = -2/3 in both equations, the point (5/3,-2/3) is indeed a solution to the system of equations.