b) Decide if the following system of e uations has zero, one or infinite solution(s). (3 Marks)
\[
\begin{array}{l}
x+4 y+2=0 \\
2 x+3 y+2=0
\end{array}
\]
\[
4 y=x-2
\]

Answer

Expert–verified

Hide Steps

Answer

\(\boxed{x = -0.4, y = -0.4}\)

Steps

Step 1 ：\(4 y=x-2\)

Step 2 ：\(A = \begin{bmatrix} 1 & 4 \\ 2 & 3 \end{bmatrix}\)

Step 3 ：\(\text{det} = -5\)

Step 4 ：\(A^{-1} = \frac{1}{\text{det}} \begin{bmatrix} 3 & -4 \\ -2 & 1 \end{bmatrix}\)

Step 5 ：\(B = \begin{bmatrix} -2 \\ -2 \end{bmatrix}\)

Step 6 ：\(X = A^{-1}B = \begin{bmatrix} -0.4 \\ -0.4 \end{bmatrix}\)

Step 7 ：\(\boxed{x = -0.4, y = -0.4}\)