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Solve using augmented matrices. $\newline$ $-5x - 7y = 1$ $\newline$ $y = 7$ $\newline$ (_, _)

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Solve a system of equations using any method

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Q. Solve using augmented matrices.

\newline

-5x - 7y = 1

\newline

y = 7

\newline

(_____, _____)

Write Augmented Matrix: First, let's write the system of equations as an augmented matrix. $\newline$ The system is: $\newline$ $-5x - 7y = 1$ $\newline$ $y = 7$ $\newline$ We can represent this as: $\newline$ $\begin{bmatrix} -5 & -7 & \vert & 1 \ 0 & 1 & \vert & 7 \end{bmatrix}$
Eliminate $y$ Term: Now, we need to use the second equation $y = 7$ to eliminate the $y$ term from the first equation. $\newline$ We can multiply the second row by $7$ and add it to the first row. $\newline$ But since the second row already represents $y = 7$ , we don't need to do any operations.
Substitute and Solve: Next, we substitute $y = 7$ into the first equation. $-5x - 7(7) = 1$ $-5x - 49 = 1$
Find $x$ : Now, we solve for $x$ . $\,-5x = 1 + 49$ $\,-5x = 50$ $\,x = 50 / (\,-5)$ $\,x = \,-10$
Final Solution: We have found the value of $x$ , and we already know the value of $y$ from the second equation. $\newline$ So, the solution to the system of equations is: $\newline$ $x = -10$ , $y = 7$

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