Eva is training for a haif-marathon and consumesenergy gels, bars and drinks every week.

Let and represents energy of gels, bars and drinks.

Weekly consumption of energy items is represented by following equations.

Total number of energy drinks .

Amount of calories consumed :

Amount of carbohydrates :

The system of equations are  

Write the equations into matrix form ,

where is coefficient matrix, is variable matrix and is constant matrix.

Definition of inverse matrix :

If is an then , where . 

Let , then .

.

, then has an inverse.

Cofactor of  is

Cofactor of

.

Find .

.

The inverse of the is

Find .

.

, and .