Page 31 - 10-Math-2 THEORY OF QUADRATIC EQUATIONS

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x2 + y2 = 7 (i) Version 1.1
2x2 + 3y2 = 18 (ii)
Multiply equation (i) with 3
3x2 + 3y2 = 21 (iii)
Subtracting equations (ii) from (iii)

Example 4: Solve the equations
x2 + y2 = 20 and 6x2 + xy - y2 = 0

Solution: Given equations are
x2 + y2 = 20 (i)
6x2 + xy - y2 = 0 (ii)
The equation (ii) can be written as
y2 - xy - 6x2 = 0

Substituting y = 3x in the equation (i), we get
x2 + (3x)2 = 20 or x2 + 9x2 = 20

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