To solve the system of equations 6x + 3y = 27 and 5x + 2y = 21 using substitution, Jon should first decide which variable would be more efficient to solve for. When deciding which variable to isolate, it's useful to see if the coefficients can be reduced by a common factor. In the first equation, the coefficients of x and y are not reducible by a common factor. However, in the second equation, both coefficients for x and y can be divided by the common factor of 1, which wouldn't clearly eliminate a variable. To solve the system most efficiently, none of the choices perfectly match the criteria of reducing by a common factor to eliminate a variable. Nevertheless, solving for y in the first equation could be slightly more convenient because the coefficient of y is smaller, resulting in simpler fractions during the calculation. To clarify, if we were to solve for y in the second equation by isolating it, we would still obtain a fraction when substituting the expression into the first equation.
The process of solving would involve the following steps:
Rearrange one of the equations to isolate y or x.
Substitute the isolated variable's expression into the other equation.
Solve the resulting equation for the remaining variable.
Substitute the found variable value into any of the original equations to solve for the second variable.
Final answer is Jon should solve for y in the first equation, as the coefficient is smaller and simplifies the calculation slightly more than if he solved for y in the second equation or for x in either equation.