## Answer :

Given system of equations:

[tex]\[ \begin{cases} x - 9y = -13 \\ 2x + y = -7 \end{cases} \][/tex]

### Step 1: Align the Equations for Elimination

We first multiply the first equation by -2 so that the coefficients of [tex]\( x \)[/tex] in both equations have opposite signs. This will allow us to eliminate [tex]\( x \)[/tex] when we add the two equations.

### Step 2: Multiply the First Equation by -2

[tex]\[ -2(x - 9y) = -2(-13) \][/tex]

[tex]\[ -2x + 18y = 26 \][/tex]

So now, the modified system of equations becomes:

[tex]\[ \begin{cases} -2x + 18y = 26 \\ 2x + y = -7 \end{cases} \][/tex]

### Step 3: Add the Equations Together

Adding the two equations results in:

[tex]\[ (-2x + 18y) + (2x + y) = 26 + (-7) \][/tex]

[tex]\[ -2x + 2x + 18y + y = 26 - 7 \][/tex]

[tex]\[ 19y = 19 \][/tex]

### Step 4: Solve for [tex]\( y \)[/tex]

[tex]\[ y = \frac{19}{19} = 1 \][/tex]

### Step 5: Substitute [tex]\( y = 1 \)[/tex] into One of the Original Equations

Now we substitute [tex]\( y = 1 \)[/tex] into the second equation [tex]\( 2x + y = -7 \)[/tex]:

[tex]\[ 2x + 1 = -7 \][/tex]

[tex]\[ 2x = -7 - 1 \][/tex]

[tex]\[ 2x = -8 \][/tex]

[tex]\[ x = \frac{-8}{2} = -4 \][/tex]

### Final Answer

By substituting back and solving, the solutions are [tex]\( x = -4 \)[/tex] and [tex]\( y = 1 \)[/tex].

Therefore, the solution to the system of equations is:

[tex]\[ \boxed{(-4, 1)} \][/tex]