Question

Solve using matrices.
5x – 6y = 50
-x + 5y = -48

Answer 1

Need help with this! I need someone to show me step by step, then ill try the others.

Answer 2

\[5x-6y = 50\\
-x +5y = -48\]
\[\begin{bmatrix}
5&-6\\
-1&5\\
\end{bmatrix}\begin{bmatrix}
x\\y
\end{bmatrix}=\begin{bmatrix}
50\\-48
\end{bmatrix}\]
\[\begin{bmatrix}
5&-6&|&50\\
-1&5&|&-48\\
\end{bmatrix}\]

Answer 3

Now, what row operation will get a 1,
into the top left element of the matrix?

Answer 4

5x – 6y = 50
-x + 5y = -48

denominator =
5 -6
-1 5
denom = 25 -6 = 19

x =
50 -6
-48 5
x = 250 -288 / denom
x = -38 / 19
x = -2

Answer 5

\[R_1\to R_1+4R_2\\
\begin{bmatrix}
1&14&|&-142\\
-1&5&|&-48\\
\end{bmatrix}\]

\[R_2\to R_2+R_1\\
\begin{bmatrix}
1&14&|&-142\\
0&19&|&-190\\
\end{bmatrix}\]

\[R_2\to R_2/19\\
\begin{bmatrix}
1&14&|&-142\\
0&1&|&-10\\
\end{bmatrix}\]

Answer 6

\[R_1\to R_1-14R_2\\
\begin{bmatrix}
1&0&|&-2\\
0&1&|&-10\\
\end{bmatrix}\]

\[\begin{bmatrix}
1&0\\
0&1\\
\end{bmatrix}\begin{bmatrix}
x\\y
\end{bmatrix}=\begin{bmatrix}
-2\\10
\end{bmatrix}\]