Which is the correct coefficient matrix for this system? 3x + 4y = 12 - x - 6y = 10

We have been given a system of equations and we are asked to write correct coefficient matrix for this system.

Since we know that a matrix for a system of equations is in the form: , where A represents the coefficient matrix, X is variables''s matrix and B is the constant matrix.          

We are given two equation and two unknown variables, so our coefficient matrix will be a matrix. Our matrices for variable and constant will be of dimensions (column matrix).

We can represent our given system of equations in matrix form as:

Now let us find our A, X and B parts from above matrices.

Since we know that A represents coefficient matrix, therefore, correct coefficient matrix for our system of equations will be,

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1

step-by-step explanation:

yes it represnts a functio, their are not 2 of the same numbers on the both sides