2x + y = -4
5x - 3y = 1

Solve with elimination method

Multiply entire first equation by 3 so the y variables will cancel when you add the equations.

6x +3y =-12
5x -3y =1

Add the equations.

11x =-11
X=-1

Now use that value for x in either equation to find y.

2(-1) +y= -4
-2+y =-4
Y =-2

Solution is (-1, -2)