Answer: x=3 and y=-1
(3,-1)
Explanation:
If the ordered pairs (x-3, 3y+1) and (y+1, x+3) are equal, it means that the x-coordinates and y-coordinates of the two pairs must be equal. Therefore, we can write:
x - 3 = y + 1 (1)
3y + 1 = x + 3 (2)
We have two equations with two variables (x and y), so we can solve for them.
From equation (1), we can solve for x in terms of y:
x = y + 4
Substituting this into equation (2), we get:
3y + 1 = (y + 4) + 3
Simplifying, we get:
2y = -2
Therefore, y = -1.
Substituting this value into equation (1), we get:
x - 3 = -1 + 1
Simplifying, we get:
x - 3 = 0
Therefore, x = 3.
Hence, the values of x and y that satisfy the condition are x = 3 and y = -1.