SOLUTION: Solve the system by addition or substitution. 3x – 4y = 8 6x – 2y = 10

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Question 28153: Solve the system by addition or substitution.
3x – 4y = 8
6x – 2y = 10
Answer by sdmmadam@yahoo.com(530)   (Show Source): You can put this solution on YOUR website!
Solve the system by addition or substitution.
3x – 4y = 8 ----(1)
6x – 2y = 10 ----(2)X 2
(Observing that the coefficients of y are (-4) and (-2) respectively, inorder to equalise the coefficients of y we find the lcm of 4 and 2 which is 4 and hence multiplying (2) through out by 2 and then subtracting the two equations we get rid of the variable y and arrive at a single simple equation in x)
3x – 4y = 8 ----(1)
12x – 4y = 20 ----(3)
(3) - (1) gives
(12x-3x)+[(-4y) - (-4y)] = 20-8
(in tests and exams you may simply do vertical subtraction mentally and write)
9x+0 = 12
9x = 12
x = 12/9 = 4/3
Putting x = 4/3 in (2), 6x-2y = 10 ----(2)
6X(4/3)-2y = 10
8-10 = 2y
-2 = 2y
y = (-2)/2 = -1
Therefore x =(4/3) and y = -1
Verification: We have put x in (2) to find y
So use (1) for verification.
Put x =(4/3) and y = -1 in (1)which is 3x – 4y = 8 ----(1)
LHS = 3x-4y = 3X(4/3) -4X(-1) = 4+4 = 8 = RHS
Therefore our values are correct



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