Students were asked to solve the equation y = x -a/b for a. Their work is shown below. Which student solved the equation correctly? Justify your answer by explaining why the other two students solved the equation incorrectly.

Question

Student 1
y = x -a / b
by = x -a
by - x = a

Student 2
y = x -a / b
y / b = x -a
y / b - x = -a
- y / b + x = a

Student 3
y = x -a/b
b y = x -a
b y -x = -a
- b y + x = a

Answer 1

Student 1 solved the equation correctly. They correctly isolated the variable a by subtracting x from both sides of the equation.

Student 2 solved the equation incorrectly. They incorrectly distributed the negative sign to both the y and x terms, resulting in a sign error. They also incorrectly isolated the variable a by subtracting x from both sides.

Student 3 solved the equation incorrectly. They incorrectly distributed the negative sign to both the y and x terms, resulting in a sign error. They also incorrectly isolated the variable a by subtracting x from both sides.

Answer 2

Show your work in your answers

Answer 3

Student 1:
Starting equation: y = x - a/b
Multiply both sides by b: by = bx - a
Add x to both sides: by + x = bx - a
Subtract bx from both sides: by - bx + x = -a
Rearrange: x - bx + by = -a
Simplify: (1 - b)x + by = -a
Therefore, a = -[(1 - b)x + by]

Student 2:
Starting equation: y = x - a/b
Multiply both sides by b: by = bx - a
Add -bx to both sides: by - bx = -a
Rearrange: -bx + by = -a
Rewrite both sides: -bx - by = a
Therefore, a = -(bx + by)

Student 3:
Starting equation: y = x - a/b
Multiply both sides by b: by = bx - a
Add x to both sides: by + x = bx - a
Subtract bx from both sides: by - bx + x = -a
Rearrange: x - bx + by = -a
Simplify: (1-b)x + by = -a
Therefore, a = -[(1-b)x + by]