Solve the following system. x² - y = 3 and x - y = -3

Solution:

The given equations are

x² - y = 3 --- (1)

x - y = -3 --- (2)

Equation (2) can be written as

y = x + 3 --- (3)

Substituting the equation (3) in (1)

⇒ x² - (x + 3) = 3

⇒ x² - x - 3 = 3

⇒ x² - x - 3 - 3 = 0

⇒ x² - x - 6 = 0

By splitting the middle term

⇒ x² + 2x - 3x - 6 = 0

Taking out the common terms

⇒ x(x + 2) - 3(x + 2) = 0

⇒ (x + 2)(x - 3) = 0

x + 2 = 0 and x - 3 = 0

x = -2 and x = 3

So if x = -2,

⇒ -2 - y = -3

⇒ -2 + 3 = y

⇒ y = 1

If x = 3

⇒ 3 - y = -3

⇒ y = 3 + 3

⇒ y = 6

Therefore, the solutions are (-2, 1) and (3, 6).

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Solve the following system. x² - y = 3 and x - y = -3

Summary:

The solutions of the system of equation x² - y = 3 and x - y = -3 are (-2, 1) and (3, 6).