SOLUTION: Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this. 8x + 10y = -34 16x � 5y = -43

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Question 371710: Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.
8x + 10y = -34
16x � 5y = -43

Found 2 solutions by mananth, Math-Help:
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
8x + 10y = -34................................1
16x � 5y = -43.................................2
..
multiply (1) by -2
-16x-20y=68
add it to (2)
16x-16x-5y-20y=-43+68
-25y=25
/-25
y=-1
...
plug value of y in (1)
8x+10y=-34
8x-10=-34
8x-34+10
8x=-24
/8
x= -3
...
m.ananth@hotmail.ca

Answer by Math-Help(7) (Show Source):
You can put this solution on YOUR website!
Elimination method requires either the "x" or "y" term to get eliminated to solve for the other remaining unknown term.
Given 8x + 10y = -34
Given 16x - 5y = -43
Action: multiply 2nd equation by 2
2(16x - 5y = -43) ==> 32x - 10y = -86
2nd Action: add this solution to 1st equation to eliminate the "y" term
8x + 10y = -34
+(32x - 10y = -86)
Sum: 40x + 0 = -120
Therefore 40x = -120
Divide both sides by 40: 40x/40 = -120/40
x = -3
Action: multiply 1st equation by 2
2(8x + 10y = -34) ==> 16x + 20y = -68
2nd Action: subtract the 2nd equation from this solution to eliminate the "x" term
16x + 20y = -68
-(16x - 5y = -43)
Difference: 0 + 25y = -25 (the -25 comes from sign change of -43 to 43-68)
Therefore 25y = -25
Divide both sides by 25: 25y/25 = -25/25
y = -1
Solution: x = -3 and y = -1.