College

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Solve for [tex]$x$[/tex] and [tex]$y$[/tex].

[tex]
\[
\begin{array}{c}
\left[
\begin{array}{ccc}
x+2 & 6 & -3 \\
9 & 18 & -6 \\
9 & -2 & y+2
\end{array}
\right]
=
\left[
\begin{array}{ccc}
2x+6 & 6 & -3 \\
9 & 18 & -6 \\
9 & -2 & x
\end{array}
\right]
\end{array}
\]
[/tex]

[tex]x = \square[/tex]

[tex]y = \square[/tex]

Answer :

To solve the matrix equation

[tex]$$
\begin{bmatrix}
x+2 & 6 & -3 \\
9 & 18 & -6 \\
9 & -2 & y+2
\end{bmatrix}
=
\begin{bmatrix}
2x+6 & 6 & -3 \\
9 & 18 & -6 \\
9 & -2 & x
\end{bmatrix},
$$[/tex]

we equate the corresponding entries from both matrices.

First, compare the [tex]$(1,1)$[/tex] entries:

[tex]$$
x+2 = 2x+6.
$$[/tex]

Subtract [tex]$x$[/tex] from both sides to isolate [tex]$x$[/tex]:

[tex]$$
2 = x+6.
$$[/tex]

Subtract [tex]$6$[/tex] from both sides:

[tex]$$
x = -4.
$$[/tex]

Next, compare the [tex]$(3,3)$[/tex] entries:

[tex]$$
y+2 = x.
$$[/tex]

Since we found [tex]$x = -4$[/tex], substitute:

[tex]$$
y+2 = -4.
$$[/tex]

Subtract [tex]$2$[/tex] from both sides to solve for [tex]$y$[/tex]:

[tex]$$
y = -6.
$$[/tex]

Thus, the solutions are:

[tex]$$
x = -4 \quad \text{and} \quad y = -6.
$$[/tex]