Let x=the larger number
y=the smaller number
If the difference of two numbers is 19,then
[tex]x - y = 19[/tex]
If the larger number is 3 more than twice the smaller,
[tex]x = 2y + 3[/tex]
subsituting
[tex]x = 2y + 3 \: to \: x - y = 19[/tex]
[tex]2y + 3 - y = 19 \\ 2y - y + 3 = 19 \\ y + 3 = 19 \\ y + 3 - 3 = 19 - 3 \\ y + 0 = 16 [/tex]
[tex]y = 16[/tex]
but ×=2y+3 so,
[tex]x = 2 (16) + 3 \\ x = 32 + 3 \\ x = 35[/tex]
Therefore, the two numbers are 16 and 35.
