A first number plus twice a second number is 55. Twice the first number plus the second totals 1313. Find the numbers.

The x=857 and y=-401

Set up the two equations

X+2y=55
2x+y=1313

Solve the system of equations by elimination

2x+y=1313
-2x-4y=-110

Add each of the corresponding terms together

-3y=1203

Divide by -3

Y=-401

Plug y back into one of the original equations

X+2(-401)=55
X-802=55
X=857