Client paid 8000 in spousal & child support. the system say that hes not allowed to claim dependent credit. ican't claim both,but can I claim just the dep.it's higher

"my client paid $3000 in spousal support and $5000.00 in child support. Since he paid for child and spousal support the system tells me that he is not allowed to claim dependent credit. I know I can't claim one, but can I claim just the dependent one since it's higher? "