1) Let's solve this Linear System of equations
y=-5x-13
x+2y=-23
2) Using the method of Substitution on the 2nd equation
x +2(-5x-13) = -23
x -10x -26= -23
-9x -26 =-23 Add 26 to both sides
9x=-23+26
9x = 3
x= 3/9
x= 1/3
y=-5(1/3) -13
y=-5/3 -13
y=-44/3
3) So there is one solution to that Linear System, different than those points (-1,-8) (4,10).