(-3, -1)
1) Solving this system by Elimination method:
Let's eliminate the x variables firstly:
-3x-5y=14 x -5 Multiply by the factor that yields the LCM (3,5) =15
-5x+7y=8 x 3 Multiply by the factor that yields the LCM (3,5) =15
15x +25y =-70
-15x +21y =24 Add both equations simultaneously
-----------------------
46y= -46 Divide both sides by 46
y= -1
2) Plug y=-1, into the smaller coefficients equation, just for convenience
-3x -5y = 14
-3x -5(-1) = 14
-3x +5=14 Subtract 5 from both sides
-3x = 9
x= -3
3) So the answer to this Linear System is (-3, -1)