Let x = the larger number

y = the smaller number

x + y = 51

x - y = 13 ==> x = y + 13

substitute y + 13 back into the first equation and solve for y

(y + 13) + y = 51

2y + 13 = 51

2y + 13 - 13 = 51 - 13

2y = 38

2y/2 = 38/2

y = 19

substitute 19 for y back into either equation

x - 19 = 13

x - 19 + 19 = 13+ 19

x = 32

substitute both x and y values back into other equation as a check

32 + 19 = 51

51 = 51

so, the larger number, x = 32, and the smaller number, y = 19

y = the smaller number

x + y = 51

x - y = 13 ==> x = y + 13

substitute y + 13 back into the first equation and solve for y

(y + 13) + y = 51

2y + 13 = 51

2y + 13 - 13 = 51 - 13

2y = 38

2y/2 = 38/2

y = 19

substitute 19 for y back into either equation

x - 19 = 13

x - 19 + 19 = 13+ 19

x = 32

substitute both x and y values back into other equation as a check

32 + 19 = 51

51 = 51

so, the larger number, x = 32, and the smaller number, y = 19