In order to solve the system of equations given, we can use substitution or elimination methods. Here’s a detailed breakdown of how to find the value of x.
Step 1: Write down the equations
- The first equation is:
3x - y = 27
- The second equation is:
3x + y = 243
Step 2: Add the equations
To eliminate y, we can add both equations together:
- (3x - y) + (3x + y) = 27 + 243
- This simplifies to:
6x = 270
Step 3: Solve for x
Now, divide both sides by 6:
- x = 270 / 6
- x = 45
Step 4: Finding the value of y
Now we can use the value of x to find y using one of the original equations. Let’s use the first equation:
- 3(45) - y = 27
- 135 - y = 27
- y = 135 - 27
- y = 108
Step 5: Check the solution
We can substitute both values back into the second equation to verify:
3(45) + 108 = 243
135 + 108 = 243
243 = 243 (True)
Thus, both equations are satisfied.
Conclusion
The value of x is confirmed to be 45. However, since the options provided were 0, 2, 4, and 6, it appears there was a misunderstanding in transcribing the original question or values. The correct value of x derived from the calculations is indeed 45. Please check the problem statement for any discrepancies.