At which coordinate point do they intersect? x+y=-2 and y=4x+3

                                              Substitution Method
 
 Step 1: Solve for either x or y in 1 of the 2 equations.

         x + y = -2 
       - x         - x 
   
          y = -x - 2 

Step 2: Plug in the expression you got for x or y into the opposite equation. 

      -x - 2 = 4x + 4
         + 2         + 2

      -x = 4x + 6 
     -4x - 4x

     -5x = 6 
       
      -5     -5

x = -6/5 

Step 3: Plug in the value for x or y into the equation you didn't use in Step 2.

           -6/5 + y = -2 
         + 6/5        + 6/5
       
            y = -4/5

(x,y) = coordinate pair
(-6/5, -4/5) = final answer