(-1, -2)
1) Let's solve that system, by the Elimination Method.
Let's eliminate the x terms on both, to begin with. Multiply the first equation by 2
x+4y= -9 x2
-2x + 3y= -4
2x+8y= -18
-2x + 3y= -4
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11y= -22 divide both sides by 11
y= -2
2) Let's plug into any of those two equations, usually the simplest one, y=-2
x +4y = -9
x +4(-2) = -9
x -8 = -9
x =-9+8
x= -1
3) Testing it:
-2x + 3y= -4
-2(-1) +3(-2) =-4
2 -6 = -4
-4 = -4 True!
Hence, the solution is (-1, -2)