8x − 6y = −20  x2
−16x + 7y = 30 
16x-12y=-40
0-5y=-10                 y=2
find the x

Let’s go step-by-step to solve this system of equations. Given the equations are:

1. \(8x - 6y = -20\)  
2. \(-16x + 7y = 30\)  
3. \(16x - 12y = -40\)  
4. \(-5y = -10\), which simplifies to \(y = 2\).

### Step 1: Find \(y\)
Since the fourth equation gives \(y = 2\), we can substitute this value of \(y\) into the other equations to find \(x\).

---

### Step 2: Substitute \(y = 2\) into the first equation
\[
8x - 6(2) = -20
\]
\[
8x - 12 = -20
\]
Add 12 to both sides:
\[
8x = -8
\]
Divide both sides by 8:
\[
x = -1
\]

---

### Step 3: Verify with other equations
Now, let’s verify that \(x = -1\) and \(y = 2\) satisfy the other equations.

- **Second equation:**  
\[
-16(-1) + 7(2) = 30
\]
\[
16 + 14 = 30
\]
This is true.

- **Third equation:**  
\[
16(-1) - 12(2) = -40
\]
\[
-16 - 24 = -40
\]
This is also true.

---

### Final Answer
The solution is:
\[
x = -1, \quad y = 2
\]

Do you need further details or have any questions?  

---

**Related Questions:**
1. How do you solve a system of equations using substitution?
2. What is the elimination method for solving systems of equations?
3. How do you determine if a system of equations has no solution or infinite solutions?
4. Can matrices be used to solve systems of equations?
5. What is Cramer's rule, and how does it apply to 2-variable systems?

**Tip:** Always substitute your solution into **all** original equations to ensure correctness.

8x − 6y = −20  x2 −16x + 7y = 30  16x -12y = -40  0 -5y = -10  y = 2 find the x

Learn how to solve a system of linear equations involving variables x and y with step-by-step substitution. This problem demonstrates key concepts like simplifying equations and verifying the solution. Suitable for students in Grades 8-10.

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