Step 1 :Define the weekly income as $2594.
Step 2 :Define the Social Security tax rate as $6.2 \%$ and the Medicare tax rate as $1.45 \%$.
Step 3 :Calculate the Social Security tax by multiplying the weekly income by the Social Security tax rate: $2594 \times 0.062 = 160.83$.
Step 4 :Calculate the Medicare tax by multiplying the weekly income by the Medicare tax rate: $2594 \times 0.0145 = 37.61$.
Step 5 :Round the results to the nearest cent: Social Security tax is $160.83$ and Medicare tax is $37.61$.
Step 6 :Final Answer: The Social Security tax is \(\boxed{160.83}\) dollars and the Medicare tax is \(\boxed{37.61}\) dollars.