What is the solution of the system of equations? x + 2y = -13 12x + 5y = -4?

you have these 2 equations
.... 1x + 2y = -13
.. 12x + 5y = -4

let's multiply the first by -12
. -12x - 24y = +156
.. 12x + 5y = -4

adding the 2 equations... (note the -12x and +12x cancel out leaving)
.. -19y = 152
..... ..y = 152/19 = -8

subbing that into either equation to solve for x
.. x = -13 - 2y
.. x = -13 + 16
.. x = 3

so the solution in (x , y) format = (3 , -8)

-5x - 10y = 65
24x + 10y = - 8____add

19x = 57
x = 3

3 + 2y = - 13
2y = - 16
y = - 8

x = 3 , y = - 8

x + 2y = -13
x = (-2y -13)
Choose either Substitution or Elimination.

substitute into 12(x) + 5y = -4
12(-2y -13) + 5y = -4
-24y -156 +5y = -4
collect like items
-19y = 152
y = -8

Put that value back into an original equation.
x + 2y = -13
x + 2(-8) = -13
x = -13 +16
x=3

So the two equations solve, or are equal, at x,y (3, -8)