y = (14x-a): 7-2. Find: a) a, if x = 6, y = 8; b) x, if y = 2, a = 42.

Brief explanation:

Step-by-step solution:

Part a) Find a, if x = 6, y = 8.

1. Substitute the given values of x and y into the equation:
   \( 8 = (14 \cdot 6 - a) : 7 - 2 \)
2. Add 2 to both sides of the equation:
   \( 8 + 2 = (14 \cdot 6 - a) : 7 \)
   \( 10 = (14 \cdot 6 - a) : 7 \)
3. Multiply both sides by 7:
   \( 10 \cdot 7 = 14 \cdot 6 - a \)
   \( 70 = 84 - a \)
4. Subtract 84 from both sides:
   \( 70 - 84 = -a \)
   \( -14 = -a \)
5. Multiply by -1 to find a:
   \( a = 14 \)

Part b) Find x, if y = 2, a = 42.

1. Substitute the given values of y and a into the equation:
   \( 2 = (14x - 42) : 7 - 2 \)
2. Add 2 to both sides of the equation:
   \( 2 + 2 = (14x - 42) : 7 \)
   \( 4 = (14x - 42) : 7 \)
3. Multiply both sides by 7:
   \( 4 \cdot 7 = 14x - 42 \)
   \( 28 = 14x - 42 \)
4. Add 42 to both sides:
   \( 28 + 42 = 14x \)
   \( 70 = 14x \)
5. Divide by 14 to find x:
   \( x = \frac{70}{14} \)
   \( x = 5 \)

Answer: a) a = 14, b) x = 5