let

x = cost of 1 large can of candied yams

y = 1 large can of cranberry sauce

5 large cans of candied yams plus 4 large cans of cranberry sauce cost a total of $36.81:

5x + 3y = 36.81

7 large cans of candied yams plus 3 large cans of cranberry sauce cost a total of $42.20:

7x + 3y = 42.20

by solving the system of equations:

5x + 3y = 36.81

7x + 3y = 42.20

we need to find x + y

2x + 3(x + y) = 36.81

4x + 3(x + y) = 42.20

multiply the first equation by (-2) on both sides and add to the second equation:

(-2)(2x + 3(x + y)) + 4x + 3(x + y) = (-2)*36.81 + 42.20

-3(x + y) = -31.42 divide both sides by (-3)

x + y = (-31.42)/(-3)

x + y = $10.47

the total cost of 1 large can of candied yams plus 1 large can of cranberry sauce is $10.47.