Question 29580

The problem should be as follows:
2x -4y = 8 ----(1)
2x - y = 1 ----(2)
(1)-(2) implies
(2x-2x)+[(-4y)-(-y)] = (8-1)
0 +(-4y+y) = 7
-3y = 7
y = (-7/3)
Putting y = (-7/3) in (1)
2x-4y = 8 ----(1)
2x-4X(-7/3) = 8
2x+28/3 = 8
2x= 8 -(28/3)
2x=(3X8-28)/3=(24-28)/3 = =(-4/3)
2x= -4/3
Therefore x = (-4/3)X(1/2)=-2/3
Answer:x= (-2/3) and y = (-7/3)
Verification: We have used (1) to find x using the value of y.
Therefore we shall use (2) for the verification.
Putting x= (-2/3) and y = (-7/3)in(2)
2x - y = 1 ----(2)
LHS= 2x-y
=2X(-2/3)-(-7/3)
=-4/3+7/3
=(-4+7)/3
=3/3
=1
=RHS
Note: Why did we subtract the equation (2) from the equation (1)
We observed that the coefficients of x in both the equation are equal in magnitude and in sign and hence subtraction would get rid of the variable x
Note: we may do the above problem using substitution method too.
2x - y = 1 ----(2) implies
(2x-1) = y ----(*)
(adding y to both the sides and subtrcting 1 from both the sides)
Putting (*) in (1),that is substituting for y in (1)
2x -4y = 8 ----(1)
2x-4X(2x-1) = 8
2x-8x+4 = 8
-6x = 8-4
-6x = 4
x = 4/(-6) =(-2/3)
Putting x=(-2/3) in (*)
y = 2x- 1 = 2X(-2/3) - 1 = -4/3-1=(-4-3)/3 = -7/3
Answer: x=-2/3 and y = -7/3
Verification: Put x=-2/3 and y = -7/3 in (1)and verify.