Complete the sentences below by dragging and dropping the correct coordinate pairs into the boxes. The graphs of $$ 2 x+y=-1 $$ and $$ -x+y=5 $$ intersect at the point The solution for the system of linear equations containing $$ 6 x+y=19 $$ and $$ x+5 y=8 $$ is

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Let's solve each system of equations to find the required points.

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### 1. Intersection of $$ 2x + y = -1 $$ and $$ -x + y = 5 $$

**Step 1:** Solve the system of equations.

$$
\begin{cases}
2x + y = -1 \
-x + y = 5
\end{cases}
$$

**Step 2:** Subtract the second equation from the first to eliminate $$ y $$.

$$
(2x + y) - (-x + y) = -1 - 5 \
2x + y + x - y = -6 \
3x = -6 \
x = -2
$$

**Step 3:** Substitute $$ x = -2 $$ into one of the original equations to find $$ y $$.

Using $$ -x + y = 5 $$:

$$
-(-2) + y = 5 \
2 + y = 5 \
y = 3
$$

**Intersection Point:** $$ (-2, 3) $$

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### 2. Solution to the System $$ 6x + y = 19 $$ and $$ x + 5y = 8 $$

**Step 1:** Express $$ y $$ from the first equation.

$$
6x + y = 19 \
y = 19 - 6x
$$

**Step 2:** Substitute $$ y = 19 - 6x $$ into the second equation.

$$
x + 5(19 - 6x) = 8 \
x + 95 - 30x = 8 \
-29x + 95 = 8 \
-29x = -87 \
x = 3
$$

**Step 3:** Substitute $$ x = 3 $$ back into $$ y = 19 - 6x $$ to find $$ y $$.

$$
y = 19 - 6(3) \
y = 19 - 18 \
y = 1
$$

**Solution:** $$ (3, 1) $$

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**Final Answers:**

1. The graphs intersect at the point **$$(-2, 3)$$**.
2. The solution for the system is **$$(3, 1)$$**.
The graphs intersect at the point $$(-2, 3)$$. The solution for the system is $$(3, 1)$$.

Complete the sentences below by dragging and dropping the correct coordinate pairs into the boxes. The graphs of \( 2 x+y=-1 \) and \( -x+y=5 \) intersect at the point The solution for the system of linear equations containing \( 6 x+y=19 \) and \( x+5 y=8 \) is

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