Here are ten systems of linear equations ready for you to solve using elimination or substitution.

Let's solve each of the 10 systems of linear equations step by step. We'll use either substitution, elimination, or matrix methods as appropriate.

---

Question 1

$$
\begin{align*}
-4x + 2y &= -12 \quad \text{(1)} \\
4x + 8y &= -24 \quad \text{(2)}
\end{align*}
$$

Step 1: Add equations (1) and (2) to eliminate $x$:

$$
(-4x + 2y) + (4x + 8y) = -12 + (-24)
\Rightarrow 10y = -36 \Rightarrow y = -3.6
$$

Now plug into equation (1):

$$
-4x + 2(-3.6) = -12 \Rightarrow -4x -7.2 = -12 \Rightarrow -4x = -4.8 \Rightarrow x = 1.2
$$

✔ Answer: $x = 1.2$, $y = -3.6$

---

Question 2

$$
\begin{align*}
4x + 8y &= 20 \quad \text{(1)} \\
-4x + 2y &= -30 \quad \text{(2)}
\end{align*}
$$

Add equations:

$$
(4x + 8y) + (-4x + 2y) = 20 + (-30) \Rightarrow 10y = -10 \Rightarrow y = -1
$$

Plug into (1):

$$
4x + 8(-1) = 20 \Rightarrow 4x - 8 = 20 \Rightarrow 4x = 28 \Rightarrow x = 7
$$

✔ Answer: $x = 7$, $y = -1$

---

Question 3

$$
\begin{align*}
x - y &= 11 \quad \text{(1)} \\
2x + y &= 19 \quad \text{(2)}
\end{align*}
$$

Add equations:

$$
(x - y) + (2x + y) = 11 + 19 \Rightarrow 3x = 30 \Rightarrow x = 10
$$

From (1): $10 - y = 11 \Rightarrow y = -1$

✔ Answer: $x = 10$, $y = -1$

---

Question 4

$$
\begin{align*}
-6x + 5y &= 1 \quad \text{(1)} \\
6x + 4y &= -10 \quad \text{(2)}
\end{align*}
$$

Add equations:

$$
(-6x + 5y) + (6x + 4y) = 1 + (-10) \Rightarrow 9y = -9 \Rightarrow y = -1
$$

Plug into (1):

$$
-6x + 5(-1) = 1 \Rightarrow -6x -5 = 1 \Rightarrow -6x = 6 \Rightarrow x = -1
$$

✔ Answer: $x = -1$, $y = -1$

---

Question 5

$$
\begin{align*}
-2x - 9y &= -25 \quad \text{(1)} \\
4x - 9y &= -23 \quad \text{(2)}
\end{align*}
$$

Subtract (1) from (2):

$$
(4x - 9y) - (-2x - 9y) = -23 - (-25)
\Rightarrow 4x - 9y + 2x + 9y = 2 \Rightarrow 6x = 2 \Rightarrow x = \frac{1}{3}
$$

Plug into (1):

$$
-2(\frac{1}{3}) - 9y = -25 \Rightarrow -\frac{2}{3} - 9y = -25 \Rightarrow -9y = -25 + \frac{2}{3} = -\frac{75}{3} + \frac{2}{3} = -\frac{73}{3}
\Rightarrow y = \frac{73}{27}
$$

✔ Answer: $x = \frac{1}{3}$, $y = \frac{73}{27}$

---

Question 6

$$
\begin{align*}
8x + y &= -16 \quad \text{(1)} \\
-3x + y &= 5 \quad \text{(2)}
\end{align*}
$$

Subtract (2) from (1):

$$
(8x + y) - (-3x + y) = -16 - 5 \Rightarrow 8x + y + 3x - y = -21 \Rightarrow 11x = -21 \Rightarrow x = -\frac{21}{11}
$$

From (2): $-3(-\frac{21}{11}) + y = 5 \Rightarrow \frac{63}{11} + y = 5 \Rightarrow y = 5 - \frac{63}{11} = \frac{55 - 63}{11} = -\frac{8}{11}$

✔ Answer: $x = -\frac{21}{11}$, $y = -\frac{8}{11}$

---

Question 7

$$
\begin{align*}
-6x + 6y &= 6 \quad \text{(1)} \\
-6x + 3y &= -12 \quad \text{(2)}
\end{align*}
$$

Subtract (2) from (1):

$$
(-6x + 6y) - (-6x + 3y) = 6 - (-12) \Rightarrow -6x + 6y + 6x - 3y = 18 \Rightarrow 3y = 18 \Rightarrow y = 6
$$

Plug into (1):

$$
-6x + 6(6) = 6 \Rightarrow -6x + 36 = 6 \Rightarrow -6x = -30 \Rightarrow x = 5
$$

✔ Answer: $x = 5$, $y = 6$

---

Question 8

$$
\begin{align*}
7x + 2y &= 24 \quad \text{(1)} \\
8x + 2y &= 30 \quad \text{(2)}
\end{align*}
$$

Subtract (1) from (2):

$$
(8x + 2y) - (7x + 2y) = 30 - 24 \Rightarrow x = 6
$$

Plug into (1):

$$
7(6) + 2y = 24 \Rightarrow 42 + 2y = 24 \Rightarrow 2y = -18 \Rightarrow y = -9
$$

✔ Answer: $x = 6$, $y = -9$

---

Question 9

$$
\begin{align*}
5x + y &= 9 \quad \text{(1)} \\
10x - 7y &= -18 \quad \text{(2)}
\end{align*}
$$

Solve (1) for $y$: $y = 9 - 5x$

Plug into (2):

$$
10x - 7(9 - 5x) = -18 \Rightarrow 10x - 63 + 35x = -18 \Rightarrow 45x = 45 \Rightarrow x = 1
$$

Then $y = 9 - 5(1) = 4$

✔ Answer: $x = 1$, $y = 4$

---

Question 10

$$
\begin{align*}
-4x + 9y &= 9 \quad \text{(1)} \\
x - 3y &= -6 \quad \text{(2)}
\end{align*}
$$

Solve (2) for $x$: $x = 3y - 6$

Plug into (1):

$$
-4(3y - 6) + 9y = 9 \Rightarrow -12y + 24 + 9y = 9 \Rightarrow -3y = -15 \Rightarrow y = 5
$$

Then $x = 3(5) - 6 = 15 - 6 = 9$

✔ Answer: $x = 9$, $y = 5$

---

✔ Final Answers Summary:

| Question | $x$ | $y$ |
|--------|------------|-------------|
| 1 | 1.2 | -3.6 |
| 2 | 7 | -1 |
| 3 | 10 | -1 |
| 4 | -1 | -1 |
| 5 | $\frac{1}{3}$ | $\frac{73}{27}$ |
| 6 | $-\frac{21}{11}$ | $-\frac{8}{11}$ |
| 7 | 5 | 6 |
| 8 | 6 | -9 |
| 9 | 1 | 4 |
| 10 | 9 | 5 |

Let me know if you'd like these in decimal form or want a graphing explanation!