Final answer:
The remainder when z is divided by 13 is 6.
Step-by-step explanation:
To find the remainder when z is divided by 13, we need to rearrange the equation to isolate z.
143x + 364y - z = 7
z = 143x + 364y - 7
Now we can substitute different integer values for x and y to find the corresponding value of z. To simplify the calculation, let's start with x = 1 and y = 0.
z = 143(1) + 364(0) - 7 = 136
The remainder when 136 is divided by 13 is 6. So, the remainder when z is divided by 13 is 6.