If 3(x - y) = 27 and 3(x + y) = 243, then the value of x is

For a system of the form a(x − y) = p and a(x + y) = q, adding the two equations eliminates y (the −ay and +ay terms cancel), giving 2ax = p + q; subtracting the equations instead eliminates x and gives the value of y. This elimination method works because both expressions are linear combinations of the same two variables.

Given:

3(x − y) = 27

3(x + y) = 243

Applying the elimination method:

1. Expand the first equation: 3(x − y) = 27 ⇒ 3x − 3y = 27

2. Expand the second equation: 3(x + y) = 243 ⇒ 3x + 3y = 243

3. Add the two expanded equations to eliminate y: (3x − 3y) + (3x + 3y) = 27 + 243 ⇒ 6x = 270

4. Solve for x: x = 270 ÷ 6 = 45

Subtracting the two expanded equations instead eliminates x: (3x + 3y) − (3x − 3y) = 243 − 27 ⇒ 6y = 216 ⇒ y = 36. Substituting x = 45 and y = 36 back into the original equations confirms both hold: 3(45 − 36) = 3 × 9 = 27, and 3(45 + 36) = 3 × 81 = 243.

Therefore, the value of x is 45.