Is there Mercy and Justice?

I have heard it said that there cannot be both mercy and justice. That justice would demand punishment, while mercy forgives punishment. And this appears to be the case when looking at the definition of these words from Meriam-Webster.

mer•cy \ˈmər-sē\ n
pl mercies [ME, fr. AF merci, fr. ML merced-, merces, fr. L, price paid, wages, fr. merc-, merx merchandise] 13c
1 a : compassion or forbearance shown esp. to an offender or to one subject to one’s power also : lenient or compassionate treatment 〈begged for mercy〉
b : imprisonment rather than death imposed as penalty for first-degree murder

2 a : a blessing that is an act of divine favor or compassion
b : a fortunate circumstance 〈it was a mercy they found her before she froze〉

3 : compassionate treatment of those in distress 〈works of mercy among the poor〉 — mercy adj —at the mercy of : wholly in the power of : with no way to protect oneself against syn mercy, charity, clemency, grace, leniency mean a disposition to show kindness or compassion. mercy implies compassion that forbears punishing even when justice demands it 〈threw himself on the mercy of the court〉. charity stresses benevolence and goodwill shown in broad understanding and tolerance of others 〈show a little charity for the less fortunate〉. clemency implies a mild or merciful disposition in one having the power or duty of punishing 〈the judge refused to show clemency〉. grace implies a benign attitude and a willingness to grant favors or make concessions 〈by the grace of God〉. leniency implies lack of severity in punishing 〈criticized the courts for excessive leniency〉.

jus•tice \ˈjəs-təs\ n
[ME, fr. AF justise, fr. L justitia, fr. justus] 12c
1 a : the maintenance or administration of what is just esp. by the impartial adjustment of conflicting claims or the assignment of merited rewards or punishments
b : judge
c : the administration of law esp : the establishment or determination of rights according to the rules of law or equity
2 a : the quality of being just, impartial, or fair
b (1) : the principle or ideal of just dealing or right action
(2) : conformity to this principle or ideal : righteousness
c : the quality of conforming to law
3 : conformity to truth, fact, or reason : correctness

But then I ran across the description of justice as described in Nelson's New Illustrated Bible Dictionary. It helps to understand the difference between terminologies today and those of Bible times.

JUSTICE — the practice of what is right and just. Justice (or “judgment,” KJV) specifies what is right, not only as measured by a code of law, but also by what makes for right relationships as well as harmony and peace.

The English term “justice” has a strong legal flavor. But the concept of justice in the Bible goes beyond the law courts to everyday life. The Bible speaks of “doing justice” (Ps. 82:3; Prov. 21:3), whereas we speak of “getting justice.” Doing justice is to maintain what is right or to set things right. Justice is done when honorable relations are maintained between husbands and wives, parents and children, employers and employees, government and citizens, and human beings and God. Justice refers to neighborliness in spirit and action.

Kings, rulers, and those in power are to be instruments of justice (Ps. 72:1), as exemplified by David (2 Sam. 8:15) and Josiah (Jer. 22:15–16). The prophet Micah declared, “He has shown you, O man, what is good; and what does the Lord require of you but to do justly, to love mercy, and to walk humbly with your God?” (Mic. 6:8). The Book of Isaiah describes God’s suffering servant, a description best fulfilled in Jesus, as one whose task as ruler will be to bring justice to the nations (Is. 42:1–4).

The prophets of the Old Testament were champions of social justice. During those days, justice was often perverted through bribery and favoritism or partiality (Deut. 1:17; Prov. 17:23). But God’s rewards come to those who practice justice in all their dealings with others. In the words of the prophet Amos, “Let justice run down like water, and righteousness like a mighty stream” (Amos 5:24).

If you ask me, I'll take justice and mercy any day over justice or mercy.