students were asked to solve the equation y= x-a/b for a their work is shown below
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
students 3:
y= x-a/b
by = x-a
by - x =-a
-by + x =a
which student solved the equation correctly justify you answer by explaining why the other two students solved the equation incorrectly
Student 1 solved the equation correctly. They correctly distributed the fraction, giving us by = x - a. They then isolated the variable by subtracting x from both sides, resulting in by - x = a.
Student 2 and Student 3 solved the equation incorrectly. In both cases, they incorrectly distributed the fraction, resulting in y/b - x = -a and -by + x = a, respectively. In both cases, they did not distribute the negative sign correctly, leading to incorrect equations.
Student 2 correctly solved the equation.
In the equation y = x - a/b, Student 2 started by dividing both sides of the equation by b, yielding y/b = x - a. Then, they subtracted x from both sides to isolate the variable, resulting in -y/b + x = a. This is the correct solution.
On the other hand, both Student 1 and Student 3 made mistakes in their solutions:
Student 1 mistakenly subtracted x from both sides of the equation, but they did not properly distribute the negative sign to the terms within the parentheses. As a result, their equation becomes by - x = a, which is incorrect.
Student 3 made a similar mistake as Student 1. They subtracted x from both sides of the equation, but again failed to distribute the negative sign to the terms within the parentheses. Therefore, their equation becomes -by + x = a, which is also incorrect.
In summary, only Student 2 correctly solved the equation because they performed the necessary operations and distributed the negative sign properly.
To determine which student solved the equation correctly, let's analyze each student's work:
Student 1:
Their work is as follows: y = x - a/b -> by = x - a -> by - x = a
Student 1 made a mistake while isolating 'a' by subtracting 'x' instead of adding it. The correct step should be by + x = a. Hence, Student 1's solution is incorrect.
Student 2:
Their work is as follows: y = x - a/b -> y/b = x - a -> y/b - x = -a
Student 2 multiplied both sides of the equation by 'b' to get rid of the fraction. However, when subtracting 'x' from both sides, they mistakenly changed the sign of 'a' to '-a'. Thus, Student 2's solution is also incorrect.
Student 3:
Their work is as follows: y = x - a/b -> by = x - a -> by - x = -a
Student 3's solution is correct. They multiplied both sides of the equation by 'b' to eliminate the fraction and then correctly subtracted 'x' from both sides. The final equation, -by + x = a, is the correct solution to the given equation.
Therefore, Student 3 solved the equation correctly, while Students 1 and 2 made errors in their calculations.