Use a matrix to find the solution to the systems of equations

The solutions of the system are:   and

Explanation

Given system of equations......

First we need to make the augmented matrix using the given equations....

Now, we need to transform the augmented matrix to the reduced row echelon form using the row operations.

Row operation 1 :   Multiply the 1st row by . So, we will get...

Row operation 2 :   Add -6 times the 1st row to the 2nd row. So, we will get...

Row operation 3 :   Multiply the 2nd row by . So, we will get...

Row operation 4 :   Add -1 times the 2nd row to the 1st row. So, we will get....

So, this is the reduced row echelon form.

We can get the equations from the above reduced row echelon form as.....

So, the solutions of the system are:   and

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.

d. vertex

step-by-step explanation: