Question 29297: solve each system using the substitution method. y-2x=-6,2y-x=5
next problem. 3a+2b=2,-2a+b=8
Answer by sdmmadam@yahoo.com(530)   (Show Source):
You can put this solution on YOUR website! y-2x=-6 ----(1)
2y-x=5 ----(2)
(1) implies y = 2x-6 ----(*)
(transposing -2x, change sign while changing side)
Putting (*) in (2),that is substituting for y
2(2x-6)-x=5
4x-12-x=5
(4x-x)= 5+12
3x=17
x=17/3
Putting x = 17/3 in (*)
y = 2x-6 = 2X(17/3)-6 = 34/3-6 = (34-18)/3 = 16/3
Answer: x = 17/3 and y = 16/3
Verification: Putting x = 17/3 and y = 16/3 in (2)
LHS = 2y-x = 32/3-17/3 = 15/3 =5 = RHS
Therefore our values are correct.
2)
3a+2b=2 ----(1)
-2a+b=8 ----(2)
(2) implies
b = 8+2a ----(*)(transposing -2a, change sign while changing side)
Putting (*) in (1),that is substituting for b
3a+2(8+2a)= 2
3a+16+4a=2
(3a+4a) = 2-16
7a = -14
a = -14/7 = -2
a=-2 in (*) implies
b = 8+2a = 8+2X(-2) = 8-4 = 4
Answer: a = -2 and b = 4
Verification: Putting a = -2 and b = 4 in (1)
LHS = 3a+2b = -6+8 = 2= RHS
Therefore our values are correct.
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