We can find the solution to this system of equations by the elimination method.

Step 1:  Subtract 2 from both sides of  4x + 18y +2 = 0

The equation becomes 4x + 18y = -2

Step 2:  Multiply all terms in the equation 4x + 18y = -2 by -4

The  equation becomes  -16x -72y = 8

Step 3:  Writing both equations in a vertical format, combine as follows:

16x + 14 y = -8

-16x  - 72y  = 8

0x  -  72y = 0

-72y =0

Dividing by -72,         y=0

Substitute 0 for y in the first equation  and solve for x as follows:

16x + 14y = -8

16x + 14(0) = -8

16x  + 0 = -8

16x = -8

Dividing by 16,           x = -1/2

Therefore our solution is  {(-1/2, 0)}

We can check our answers by substituting the values for x and y into both equations.

16x + 14y = -8

16(-1/2) + 14(0) = -8

-8 = -8

4x + 18y + 2 =0

4(-1/2) + 18(0) + 2 = 0

-2 +  0 + 2  = 0

0=0

Eliminating is my favorite part of solving equations!