Answer:Kathy is correct
Step-by-step explanation: We need to solve both equations separately in order to determine with certainty which one is correct and which one is not.
Kevin thinks the new equation should be
3(6x-1) + 2y = 43
This can now be solved as follows;
18x - 3 + 2y = 43
Add 3 to both sides of the equation
18x - 3 + 3 + 2y = 43 + 3
18x + 2y = 46
2(9x + y) = 46 (factorize the left hand side of the equation by 2)
Divide both sides of the equation by 2
9x + y = 46
The variables remain unsolved
On the other hand, Kathy thinks the new equation should be
3x + 2(6x - 1) = 43
This can now be solved as follows;
3x + 12x - 2 = 43
Collect like terms (in this equation, x)
15x - 2 = 43
Add 2 to both sides of the equation
15x - 2 + 2 = 43 + 2
15x = 45
Divide both sides of the equation by 15
x = 3
In essence, Kathy's equation has a solution (x=3) while that of Kevin remains unsolved
