Question

Solve the system of equations using the matrix equation given. What is y equal to? Explain the steps that you took to solve this problem.

Answer 1

The solution of the system of linear equations is (x, y) = (4, 0).

How to resolve a system of linear equations

There are several methods to solve linear equations, one of the quickest is the determinant methods, which uses linear algebraic structures known as determinants. Now we proceed to solve the system and we start looking up for the variable y:

Step 1 - Determine the determinant of the matrix of dependent coefficients:

$D = \left|\begin{array}{cc}2&9\\2&8\end{array}\right|$

D = 2 · 8 - 2 · 9

D = 16 - 18

D = - 2

Step 2 - Replace the elements of the second column with the elements of vector column of independent coefficients:

$D_{2} = \left|\begin{array}{cc}2&8\\2&8\end{array}\right|$

D₂ = 2 · 8 - 2 · 8

D₂ = 0

Step 3 - Divide the determinant found in the previous step by the determinant of the matrix of dependent coefficients:

y = D₂ / D

y = 0

And finally we look up for the variable x:

Step 1 - Determine the determinant of the matrix of dependent coefficients:

D = - 2

Step 2 - Replace the elements of the second column with the elements of vector column of independent coefficients:

$D_{1} = \left|\begin{array}{cc}8&9\\8&8\end{array}\right|$

D₁ = 8 · 8 - 8 · 9

D₁ = 64 - 72

D₁ = - 8

Step 3 - Divide the determinant found in the previous step by the determinant of the matrix of dependent coefficients:

x = D₁ / D

x = (- 8) / (- 2)

x = 4

The solution of the system of linear equations is (x, y) = (4, 0).

To learn more on systems of linear equations: brainly.com/question/19549098

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