Question

How to solve this using the elimination method

Answer 1

10x+2y=18
10x-7y=-18
Multiply the second one by -1
-10x+7y=18
Then add the two equations 
  10x+2y=18
+-10x+7y=18
----------------
9y=36
y=4

Plug that back into one of the equations above and solve for x
10x+2y=18
10x+2(4)=18
10x+8=18
10x=10
x=1

so your answer is x=1 and y=4 or (1,4)