Question 75635
PROCESS OF ELIMINATION WOULD BE MY VOTE.
MULTIPLY EQUATION #1 BY 2 & EQUATION #2 BY -5.
2(5X-2Y=7), 10X-4Y=14
-5(2X+5Y=-3), -10-25Y=15 NOW ADD THESE 2 EQUATIONS THUS:
10X-4Y=14
-10X-25Y=15
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0X-29Y=29
Y=29/-29
Y=-1 ANSWER.
NOW SUBSTITUTE -1 FOR Y AND SOLVE FOR X
5X-2*-1=7
5X+2=7
5X=7-2
5X=5 
X=5/5
X=1 ANSWER.
PROOF
2*1+5*-1=-3
2-5=-3
-3=-3