Find the solution of the system of equations. $$ \begin{array}{r}-x-7 y=-41 \ \qquad x-6 y=-37\end{array} $$ Answer Attempt 1 out of 2

Question

UpStudy AI · Accepted Answer

We start with the system of equations:
$$
\begin{aligned}
- x - 7y &= -41, \
\quad x - 6y &= -37.
\end{aligned}
$$

**Step 1.** Add the two equations to eliminate $$ x $$:

$$
(- x - 7y) + (x - 6y) = -41 + (-37).
$$

Notice that $$ -x + x = 0 $$ and $$ -7y - 6y = -13y $$. Thus, the equation simplifies to:

$$
-13y = -78.
$$

**Step 2.** Solve for $$ y $$:

$$
y = \frac{-78}{-13} = 6.
$$

**Step 3.** Substitute $$ y = 6 $$ into one of the original equations. We choose the second equation:

$$
x - 6y = -37.
$$

Replace $$ y $$ by 6:

$$
x - 6(6) = -37 \quad \Rightarrow \quad x - 36 = -37.
$$

**Step 4.** Solve for $$ x $$:

$$
x = -37 + 36 = -1.
$$

**Solution:** The solution to the system is:
$$
(x, y) = (-1, 6).
$$
The solution to the system is $$ x = -1 $$ and $$ y = 6 $$.

Find the solution of the system of equations. \[ \begin{array}{r}-x-7 y=-41 \\ \qquad x-6 y=-37\end{array} \] Answer Attempt 1 out of 2