Make a system of equations.
[tex]\sf~x=3y+2[/tex]
[tex]\sf~x+y=22[/tex]
Re-arrange the 2nd equation:
[tex]\sf~x+y=22[/tex]
Subtract y to both sides:
[tex]\sf~x=-y+22[/tex]
Plug in -y + 22 for 'x' in the first equation.
[tex]\sf~x=3y+2[/tex]
[tex]\sf~-y+22=3y+2[/tex]
Subtract 3y to both sides:
[tex]\sf~-4y+22=2[/tex]
Subtract 22 to both sides:
[tex]\sf~-4y=-20[/tex]
Divide -4 to both sides:
[tex]\sf~y=\boxed{\sf5}[/tex]
Plug this into any of the two equations to find 'x':
[tex]\sf~x+y=22[/tex]
[tex]\sf~x+5=22[/tex]
Subtract 5 to both sides:
[tex]\sf~x=\boxed{\sf17}[/tex]
So one of the numbers is 5 and one of them is 17.
