SOLUTION: Solving using the substitution method: 8x - 5y = -47 4x + 3y = -7 I got some help from the site, but I dont know how it derived to that answer. When doing it long hand, I c

Question 272377: Solving using the substitution method:
8x - 5y = -47
4x + 3y = -7
I got some help from the site, but I dont know how it derived to that answer. When doing it long hand, I couldn't get the same results.
Expressing x as a function of y (from the first equation) x = (-47 +5y)/8
Substituting this expression into the second equation:
4(-47-5y)/8+3y = -7
Simplifying this expression:
44y = 132 or y = 3
Now, substituting y = 3 back into the x expressed as a function of y:
x = (-47+5y)/8 = -4

Found 2 solutions by scott8148, checkley77:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
take advantage of easy ratios of coefficients

4x + 3y = -7 ___ 4x = -3y - 7

2(4x) - 5y = -47

substituting ___ 2(-3y - 7) - 5y = -47

-6y - 14 - 5y = -47

-11y = -33 ___ y = 3

substituting ___ 4x = -3(3) - 7 ___ 4x = -16 ___ x = -4
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
8x - 5y = -47
8X=5Y-47
X=(5Y-47)/8
4x + 3y = -7
4(5Y-47)/8+3Y=-7
(20Y-188)/8+3Y=-7
(20Y-188+3Y*8)/8=-7
20Y-188+24Y=-56
44Y=-56+188
44Y=132
Y=132/44
Y=3 ANS.
X=(5*3-47)/8
X=(15-47)/8
X=-32/8
X=-4 ANS.
PROOF:
4*-4+3*3=-7
-16+9=-7
-7=-7

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