Answered

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What are the x coordinates of the solutions to the system of equations . - x + y = 2 y = x^2 - 4

Sagot :

Given:

-x + y = 2

y = x² - 4

Make y subject of formula in the first equation.

y = x + 2

Substitute into the second equation.

x + 2 = x² - 4

Subtract x+2 from both-side of the equation.

x²- 4 - x - 2 = 0

x² - x - 4 - 2 = 0

x² - x - 6 = 0

Solve for x using factorisation method.

Replace the coefficient of x by two numbers whose product gives -6 and sum gives -1.

That is;

x² - 3x + 2x - 6 = 0

x(x- 3) + 2 ( x - 3) = 0

(x-3)(x+2) = 0

Either x - 3 = 0

⇒x = 3

OR

x + 2 = 0

⇒ x = -2

Therefore, the coordinates of x are -2 and 3.

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