What is the point of intersection of the lines 16x+14y=-8 and 4x+18y+2=0 ?

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!