# algebra

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x^2+4y^2=25
y^2-x=1

• algebra -

Eq1: X^2 + 4Y^2 = 25.

Eq2: Y^2 - X = 1.
Y^2 = X + 1.

In Eq1, substitute

• algebra -

Eq1: X^2 + 4Y^2 = 25.

Eq2: Y^2 - X = 1.
Y^2 = X + 1.

In Eq1, substitute X+1 for Y^2:
X^2 + 4(X+1) = 25,
X^2 + 4X + 4 = 25,
(X+2)^2 = 25,
Take sqrt of both sides:
X+2 = +-5,
X = X = 5-2 = 3.
X = -5-2 = -7.

Solution set: (3,+-2), (-7,+-sqrt6i).

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