Question

Solve the system by using elementary row operations on the equations. Follow the systematic elimination procedure
x1+4x2 =11
2x1+7x2=18
Find the solution to the system of equations.

Answer 1

Answer:

The solution of the Given matrix

  ( x₁ ,    x ₂ ) = ( - 5 , 4 )

Step-by-step explanation:

Step(i):-

Given equations are  x₁+4 x₂ = 11 ...(i)

                                 2 x₁ + 7 x₂= 18 ...(ii)

The matrix form

                                A X = B

            $\left[\begin{array}{ccc}1&4\\2&7\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}11\\8\\\end{array}\right]$

Step(ii):-

      $\left[\begin{array}{ccc}1&4\\2&7\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}11\\8\\\end{array}\right]$

The Augmented Matrix form is

$[AB] = \left[\begin{array}{ccc}1&4&11\\2&7&18\\\end{array}\right]$

Apply Row operations,  R₂ → R₂-2 R₁

$[AB] = \left[\begin{array}{ccc}1&4&11\\0&-1&-4\\\end{array}\right]$  

The matrix form

                   $\left[\begin{array}{ccc}1&4\\0&-1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}11\\-4\\\end{array}\right]$

The equations are

                     x₁ + 4 x₂ = 11 ...(a)

                         - x ₂ = - 4

                            x ₂ = 4

Substitute   x ₂ = 4 in equation (a)

                      x₁ + 4 x₂ = 11

                      x₁ = 11 - 16

                        x₁ = -5

Final answer:-

The solution of the Given matrix

  ( x₁ ,    x ₂ ) = ( - 5 , 4 )