To solve this system of equations:  
1. \( 10x - y = 9 \)  
2. \( -3x + 2y = -4 \)  

We can use **substitution** or **elimination**. Let's solve it step-by-step using **elimination**.

---

### Step 1: Align the equations
\[
10x - y = 9 \tag{1}
\]
\[
-3x + 2y = -4 \tag{2}
\]

---

### Step 2: Eliminate one variable
Let's eliminate \(y\) by multiplying both equations so the coefficients of \(y\) are the same.

- Multiply (1) by 2:
\[
2(10x - y) = 2(9) \quad \Rightarrow \quad 20x - 2y = 18
\]
- Leave equation (2) as is:
\[
-3x + 2y = -4
\]

Now, add the two equations:
\[
(20x - 2y) + (-3x + 2y) = 18 + (-4)
\]
\[
20x - 3x = 14 \quad \Rightarrow \quad 17x = 14
\]
\[
x = \frac{14}{17}
\]

---

### Step 3: Solve for \(y\)
Now that we know \(x = \frac{14}{17}\), substitute this value into one of the original equations. Let’s use equation (1):
\[
10x - y = 9
\]
\[
10\left(\frac{14}{17}\right) - y = 9
\]
\[
\frac{140}{17} - y = 9
\]
First, isolate \(y\):
\[
-y = 9 - \frac{140}{17}
\]
Express 9 as a fraction with denominator 17:
\[
9 = \frac{153}{17}
\]
Now subtract:
\[
9 - \frac{140}{17} = \frac{153 - 140}{17} = \frac{13}{17}
\]
Thus:
\[
-y = \frac{13}{17} \quad \Rightarrow \quad y = -\frac{13}{17}
\]

---

### Step 4: Solution
The solution to the system of equations is:
\[
x = \frac{14}{17}, \quad y = -\frac{13}{17}
\]

---

Do you have any questions or need further clarification?

Here are 5 related questions:
1. How do we solve systems of equations using substitution?
2. What are the advantages of elimination over substitution?
3. How can systems of equations be solved graphically?
4. What happens if a system of equations has no solution?
5. How do we recognize a system of dependent equations?

**Tip:** Always double-check your solution by substituting the values of \(x\) and \(y\) into the original equations.

Learn how to solve the system of equations 10x - y = 9 and -3x + 2y = -4 with a step-by-step solution using the elimination method. This solution involves aligning equations, eliminating variables, and finding the values of x and y. Ideal for students in Grades 8-10, this problem covers key algebra concepts.

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