Given:
[tex]A=\begin{bmatrix}{4} & {5} & {-6} \\ {3} & {-2} & 7 \\ {7} & {-6} & -8\end{bmatrix}^{-1}\begin{cases}{-14} \\ {47} \\ {15}\end{cases}[/tex]Required:
We want to find y-value
Explanation:
To find inverse
First we need to find adj of given matric
[tex]adj(A)=\begin{bmatrix}{58} & {7}3 & {-4} \\ {76} & {10} & {59} \\ {23} & {-46} & {-23}\end{bmatrix}[/tex]Now find determinent of matrix A
[tex]\begin{gathered} A=4(16-(-42))-5(-18-49)-6(-18+14) \\ =4*58-5*-73-6(-4) \\ =232+367+24=621 \end{gathered}[/tex]now put the values
[tex]\begin{gathered} \frac{1}{621}\begin{bmatrix}{58} & {73} & {-4} \\ {76} & {10} & {59} \\ {23} & {-46} & {-23}\end{bmatrix}\begin{cases}{-14} \\ {47} \\ {15}\end{cases} \\ \\ =\frac{1}{621}\begin{cases}{2559} \\ {291} \\ {2829}\end{cases} \end{gathered}[/tex]Final answer:
A