How can oxidation numbers be used to balance chemical equations?

[Witcher]

Homework Statement

I have been on letter A problem for hours now and can’t seem to balance the equation.

Relevant Equations

It is a combustion reaction i think because both sides have oxygen and hydrogen

I attached my attempt and the question from the book, as you can see i kept failing because my hydrogens wouldn't balance and neither would my oxygens.

 

[BvU]

I can't read the pictures: they are rotated 90 degrees to the right. Please put hem upright, or better: type them out.

 

[Borek]

A is not a combustion reaction though.

 

[Chestermiller]

You can do example (a) algebraically. Write the balanced equation as $$aN_2H_4+bH_2O_2=cHNO_3+dH_2O$$Based on this, what is the balance on nitrogen atoms? What is the balance on H atoms? What is the balance on O atoms? Solve these 3 equations in 4 unknowns for b, c, and d in terms of a. What do you get?

 

[mjc123]

This one may be simpler if you go by oxidation numbers, noting that total oxidation number is conserved.
Hint: oxygen goes from -1 to -2 (in both products); nitrogen goes from -2 to +5; H doesn't change.