Twice a number plus twice a second number is 310. The difference between the numbers is 55. Find the numbers by writing and solving a system of equations.

2x+2y=310

x-y=55

multiply seond equation by 2 and adding to first equation

2x-2y=110

add

2x-2y=110

2x+2y=310 +

4x+0y=420

4x=420

divide 4

x=105

sub

x-y=55

105-y=55

minuse 105

-y=-50

mult - 1

y=50

the numbers are 105 and 50