The solution to a system of equations is $$ (5,-19) $$. Select the two equations that could make up the system. $$ \square \begin{array}{l}y=-7 x+16 \ \square \ \square=-3 x-6 \ y=-2 x-9 \ \square \ y=-x-17 \ y=2 x-23\end{array} $$

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To determine which two equations from the list have the solution $$ (5, -19) $$, we'll substitute $$ x = 5 $$ and $$ y = -19 $$ into each equation to see which ones are satisfied.

1. **$$ y = -7x + 16 $$**
   $$
   -19 = -7(5) + 16 \
   -19 = -35 + 16 \
   -19 = -19 \quad \text{✓}
   $$
   This equation is satisfied by $$ (5, -19) $$.

2. **$$ y = -3x - 6 $$**
   $$
   -19 = -3(5) - 6 \
   -19 = -15 - 6 \
   -19 = -21 \quad \text{✗}
   $$
   This equation is **not** satisfied by $$ (5, -19) $$.

3. **$$ y = -2x - 9 $$**
   $$
   -19 = -2(5) - 9 \
   -19 = -10 - 9 \
   -19 = -19 \quad \text{✓}
   $$
   This equation is satisfied by $$ (5, -19) $$.

4. **$$ y = -x - 17 $$**
   $$
   -19 = -5 - 17 \
   -19 = -22 \quad \text{✗}
   $$
   This equation is **not** satisfied by $$ (5, -19) $$.

5. **$$ y = 2x - 23 $$**
   $$
   -19 = 2(5) - 23 \
   -19 = 10 - 23 \
   -19 = -13 \quad \text{✗}
   $$
   This equation is **not** satisfied by $$ (5, -19) $$.

**Conclusion:**
The two equations that are satisfied by $$ (5, -19) $$ are:

$$
\boxed{\begin{aligned}
y &= -7x + 16 \
y &= -2x - 9
\end{aligned}}
$$
The two equations that have the solution $$ (5, -19) $$ are: $$ y = -7x + 16 \quad \text{and} \quad y = -2x - 9 $$

The solution to a system of equations is . Select the two equations that could make up the system.

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