To determine the values of X and Y, we can solve the given system of equations using elimination.
**Method 1: Elimination**
1. Add the first and second equations:
```
4X + 2Z = 10
2. Subtract the second equation from the third equation:
X = 7
3. Substitute X = 7 into the first equation:
3(7) + Y + Z = 8
21 + Y + Z = 8
Y + Z = -13
4. Solve for Y and Z:
Y = -13 - Z
Substitute this expression for Y in the second equation:
X - (-13 - Z) + Z = 2
7 + 13 + Z + Z = 2
2Z = -18
Z = -9
5. Substitute Z = -9 back into the expression for Y:
Y = -13 - (-9)
Y = -4
Therefore, the values of X and Y are X = 7 and Y = -4.
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To determine the values of X and Y, we can solve the given system of equations using elimination.
**Method 1: Elimination**
1. Add the first and second equations:
```
4X + 2Z = 10
```
2. Subtract the second equation from the third equation:
```
X = 7
```
3. Substitute X = 7 into the first equation:
```
3(7) + Y + Z = 8
21 + Y + Z = 8
Y + Z = -13
```
4. Solve for Y and Z:
```
Y = -13 - Z
```
Substitute this expression for Y in the second equation:
```
X - (-13 - Z) + Z = 2
7 + 13 + Z + Z = 2
2Z = -18
Z = -9
```
5. Substitute Z = -9 back into the expression for Y:
```
Y = -13 - (-9)
Y = -4
```
Therefore, the values of X and Y are X = 7 and Y = -4.