Kevin and his sister, katy, are trying to solve the system of equations . keven thinks the new equation should be 3(6x-1)+2y=43 , while katy thinks it should be 3x+2(6x-1)=43.who is correct and why

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

answer: t=3

step-by-step explanation: