In one day, joe consumes 530 calories by drinking 1 serving of juice, 2 servings of milk, and 1 soda. darius consumes 370 calories by drinking 2 servings of juice and 1 serving of milk. marian consumes 510 calories by drinking 3 servings of milk and 1 soda. using matrices to solve, how many calories are in 1 serving of milk? 90 110 130 180

110

Step-by-step explanation:

Let x represent the amount of calories in juice, y represent the amount of calories in milk and z represent the amount of calories in soda.

The first equation will then be

1x+2y+1z = 530.

The second equation will be

2x+1y+0z = 370.

The third equation will be

0x+3y+1z = 510

The coefficient matrix, formed by the coefficients of the variables in the equation, will be

.

The variable matrix will be

.

The constant matrix, formed by the constants of each equation, will be

Together, we have

To solve this, we find the inverse of the coefficient matrix:

We multiply both sides of the equation by this:

This leaves us with the coefficient matrix on the left, and the following matrix on the right:

This means x = 130, y = 110 and z = 180.

Since y represents the number of calories in the milk, there were 110 calories per serving in the milk.

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction