Question

Identify the augmented matrix for the system of equations and the solution using row operations.

Answer 1

Given:

The system of equation is given as,

`\begin{gathered} 7x-4y=28 \\ 5x-2y=17 \end{gathered}`

The objective is identify the augmented matrix for the system of equations and the solution using row operations.

Step-by-step explanation:

The required augmented matrix will be,

Performing the Gauss-Jordan elimination with the following operation,

`R_2=R_2-(5R_1)/(7)`

By applying the operation to the augmented matrix,

To find y :

On equating the second row of the matrix,

`\begin{gathered} (6y)/(7)=-3 \\ y=(-3)/((6)/(7)) \\ y=(-3*7)/(6) \\ y=(-7)/(2) \end{gathered}`

To find x :

On equating the first row of the matrix,

`\begin{gathered} 7x-4y=28 \\ 7x=28+4y \\ x=(28+4y)/(7) \end{gathered}`

Substitute the value of y in the above equation.

`\begin{gathered} x=(28+4((-7)/(2)))/(7) \\ x=(28-14)/(7) \\ x=(14)/(7) \\ x=2 \end{gathered}`

Thus the value of solutions are,

`\begin{gathered} x=2 \\ y=-(7)/(2)=-3.5 \end{gathered}`

Hence, option (3) is the correct answer.