4x2
+ y2 = 10 --------------------- (1)
2x + y = 4 ------------------------ (2)
You may find
that if you square (2), the square terms will be same as that in (1). This will
help us to extract the value of xy.
So, lets’
first square Eq (2)
We get 4x2
+ y2 + 4xy = 16 --------- (3)
Substitute
Eq (1) in (3), we get
10 + 4xy =
16
Or, xy = 6/4 ---------------- (4)
Now whenever
we find a situation here the value of a + b and ab is given, we find a – b using
the good old formulae
( a – b)2
= (a + b)2 – 4ab
Applying
this concept, we get
(2x – y)2
= (2x + y)2 – 4.2x.y
Now, substitute
the values on RHS of equation with
values from (2) and (4)
(2x – y)2
= 42 – 4.2.6/4 = 4
Or, 2x – y =
2 ------------------------- (5)
Now, simply
solve equation (2) and (5) by adding the two equations
We get 4x =
6
Or x = 3/2
Therefore, y
= 1
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