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pake cara eliminasi sama substitusi, btw ini soal psltv

The problem involves solving a system of linear equations using elimination and substitution. The equations are:

1. \( 2x + 3y - z = 9 \)
2. \( 3x + 2y + z = 16 \)
3. \( 2x + y = 7 \)

Let’s solve it step by step using elimination and substitution:

---

### **Step 1: Simplify Equation (3)**
From Equation (3), solve for \( y \) in terms of \( x \):
\[
y = 7 - 2x \tag{4}
\]

---

### **Step 2: Eliminate \( z \) Using Equations (1) and (2)**
Add Equations (1) and (2):
\[
(2x + 3y - z) + (3x + 2y + z) = 9 + 16
\]
\[
5x + 5y = 25 \tag{5}
\]

From Equation (5), simplify:
\[
x + y = 5 \tag{6}
\]

---

### **Step 3: Substitute \( y \) From Equation (4) Into Equation (6)**
Substitute \( y = 7 - 2x \) into \( x + y = 5 \):
\[
x + (7 - 2x) = 5
\]
\[
x + 7 - 2x = 5
\]
\[
-x + 7 = 5
\]
\[
x = 2 \tag{7}
\]

---

### **Step 4: Find \( y \) Using Equation (4)**
Substitute \( x = 2 \) into \( y = 7 - 2x \):
\[
y = 7 - 2(2)
\]
\[
y = 3 \tag{8}
\]

---

### **Step 5: Find \( z \) Using Equation (1)**
Substitute \( x = 2 \) and \( y = 3 \) into Equation (1):
\[
2(2) + 3(3) - z = 9
\]
\[
4 + 9 - z = 9
\]
\[
13 - z = 9
\]
\[
z = 4 \tag{9}
\]

---

### **Final Solution**
The values of \( x, y, z \) are:
\[
x = 2, \quad y = 3, \quad z = 4
\]

---

Would you like a detailed verification of the solution or further explanation? 

---

### **Related Questions**
1. How does elimination work when there are no directly cancelable terms?
2. How would substitution differ if solving from another equation?
3. What is a geometric interpretation of these three equations?
4. Can we use matrix methods like Gaussian elimination here?
5. How do we check if this system of equations has a unique solution?

### **Tip**
Always verify your final solution by substituting the values of \( x, y, z \) into **all original equations**!

Tentukan nilai x, y, dan z menggunakan metode eliminasi dan substitusi pada sistem persamaan linier tiga variabel (SPLTV).

Learn how to solve a system of linear equations involving three variables using the elimination and substitution methods. Includes step-by-step solutions for finding x, y, and z.

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