Question

1. $x + 9y = -8$; $-x - 8y = 7$ 6) $7x - 7y = -14$; $-2x + 7y = -16$ 8) $x + 7y = 3$; $4x + 7y = -9$

Explanation:

Let's solve problem 6: the system of equations \(7x - 7y = -14\) and \(-2x + 7y = -16\).

Step 1: Add the two equations to eliminate \(y\)

Adding \(7x - 7y = -14\) and \(-2x + 7y = -16\) gives:
\[

$$\begin{align*} (7x - 7y) + (-2x + 7y) &= -14 + (-16)\\ 7x - 7y - 2x + 7y &= -30\\ 5x &= -30 \end{align*}$$

\]

Step 2: Solve for \(x\)

Divide both sides of \(5x = -30\) by 5:
\[
x = \frac{-30}{5} = -6
\]

Step 3: Substitute \(x = -6\) into the first equation to find \(y\)

Substitute \(x = -6\) into \(7x - 7y = -14\):
\[

$$\begin{align*} 7(-6) - 7y &= -14\\ -42 - 7y &= -14 \end{align*}$$

\]

Step 4: Solve for \(y\)

Add 42 to both sides:
\[
-7y = -14 + 42 = 28
\]
Divide both sides by \(-7\):
\[
y = \frac{28}{-7} = -4
\]

Answer:

The solution to the system is \(x = -6\) and \(y = -4\).