Question

Solve the equation by inversion method, 2x + 6y = 8, x + 3y = 5

Answer 1

2x + 6y = 8

x + 3y = 5

Write in matrix form:

$\left(\begin{array}{cc}2 \ \ 6 \\ 1 \ \ 3 \end{array}\right)\left(\begin{array}{cc}x\\y\end{array}\right) = \left(\begin{array}{cc}8\\5\end{array}\right)$

Find the determinant:

$\left|\begin{array}{cc}2 \ \ 6 \\ 1 \ \ 3 \end{array}\right| = (2)(3) - (1)(6) = 0$

Since the determinant is zero,

⇒ The two equations are linearly dependent.

⇒ One equation is a multiplier of the other

⇒ There is no solution