Given the system of equations: 2x – y = –2 x = 14 + 2y what is the value of the system determinant? what is the value of the y−determinant? what is the value of the x−determinant? what is the solution to the system of equations?

ANSWER 1

The given system  of equations is:

Let us rewrite the second system to obtain,

We need to apply the Cramer's rule. So we write out the coefficient matrices to obtain:

The answer column is;

The value of the y-determinant is denoted by . To find this we replace the coefficient determinant with answer-column values in y-column to get,

Recall that,

If

then,

This implies that,

ANSWER 2

The value of the x-determinant is denoted by . To find this we replace the coefficient determinant with answer-column values in x-column to get,

This implies that,

ANSWER 3

To find the solution to the system of equations.

We need to find the determinant of the coefficient matrix.

This implies that,

Cramer's rule says that,

and

Therefore the solution is and  .

step-by-step explanation:

fabric (square meters)                   cloaks

7                                                           21

4/3                                                         4

step-by-step explanation:

we are told that harry needs 2 square meters of fabric for every 6 wizard cloaks he makes.

1. first of all we will find how many cloaks can be made from 1 square meter of fabric by dividing 6 by 2.

we can see that 3 cloaks can be made from 1 square meter of fabric. now we will multiply 3 by 7 to find number of cloaks made from 7 square meters of fabric.

therefore, harry will make 21 cloaks from 7 square meters of fabric.

2. let us find how many square meters of fabric will be needed to make 4 cloaks.

first of all we will find fabric needed for 1 cloak by dividing 2 by 6.

we can see that fabric needed for 1 cloak is   square meter. now we will multiply   by 4 to find fabric needed for 4 cloaks.