The sum of two numbers is 22. three times one number increased by five is the same as twice the other number decreased by four. what is the larger of the two numbers?

X+y=22

3x+5=2y-4

cool

3x+5=2y-4

add 4 to both sides

3x+9=2y

minus 2y both sides and minus 9 both sides

3x-2y=-9

multiply first equation by 2 and add to 2nd

2x+2y=44

3x-2y=-9 +

5x+0y=35

5x=35

divide both sides by 5

x=7

sub back

x+y=22

7+y=22

minus 7

y=15

the bigger one is 15