The sum of five times a number and twice a second number is 18, but the difference of three times the first number and seven times the second number is -22. find the two numbers using the elimination method.

X and y are the numbers
sum means add
5x+2y=18
3x-7y=-22

ok, eliminat
eliminate x's
multiply top by 3 and bottom by -5 and add them equation

15x+6y=54
-15x+35y=110+
0x + 41y=164

41y=164
divide both sides by 41
y=4

sub back

5x+2y=18
5x+2(4)=18
5x+8=18
minus 8
5x=10
divide 5
x=2

the first number is 2, the 2nd number is 4