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