Solve the system: y^2 - x^2 = 9 2x - y = 3

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llltkl | College Teacher | (Level 3) Valedictorian

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Let `y^2 - x^2 = 9`   ..........eq. (i)

`2x - y = 3` .........eq.(ii)

From (ii) we get:


Substituting `y=2x-3` in eq. (i) we get:


`rArr 4x^2-12x+9-x^2-9=0`

`rArr 3x^2-12x=0`

`rArr 3x(x-4)=0`

So, either x=0 or x=4

Now plug in the values of x in eq.(ii) to get the corresponding values of y.

So, when x=0    `y=2*0-3=-3`

When x=4       `y=2*4-3=5`

Therefore, the solutions are (0,-3) and (4,5).