SOLUTION: Solve by elimination addition method 12x+5y=2, -2x+3y=15

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Question 1101918: Solve by elimination addition method 12x+5y=2, -2x+3y=15
Found 2 solutions by Katarekt, ikleyn:
Answer by Katarekt(3) About Me  (Show Source):
You can put this solution on YOUR website!
12x+5y=2 (eq. 1)
-2x+3y=5 (eq. 2)
Eq 2 x6
12x+5y=2
-12x+18y=20
eq. 2+eq.1
5y+18y=20+2
23y=22
y=+22%2F23+
Sub y into eq. 1 (or eq. 2, but I'm using eq. 1)
12x+5(+22%2F23+)=2
12x++110%2F23+=2
12x=2-+110%2F23+
12x=+-%2864%2F23%29+
x=+-%2816%2F69%29+
x= +-%2816%2F69%29+, y=+22%2F23+

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
 12x + 5y =  2,     (1)
 -2x + 3y = 15.     (2)


Multiply eq(2) by 6 (both sides). The modified system is

 12x + 5y =   2,    (3)
-12x + 18y = 90.    (4)


Now add equations (3) and (4). You will get

5y + 18y = 2 + 92  ====>  23y = 94  ====>  y = 92%2F23 = 4.

Then from eq(2) -2x = 15 - 3y = 15 - 3*4 = 3  ====>  x = 3%2F%28-2%29 = -3/2.


Answer.  x = -3/2,  y = 4.