What are the x-coordinates of the solutions to this system of equations?
x² + y² = 36, y = x - 6.

Solution:

Given system of equations are

x² + y² = 36 --- (1)

y = x - 6 --- (2)

Replace y from equation 2 in equation 1,

⇒ x² + (x - 6)² = 36

Expanding (x - 6)² using (a - b)² = a² + b² - 2ab

⇒ x² + x² - 12x + 36 = 36

⇒ 2x² - 12x = 0

⇒ 2x(x - 6) = 0

⇒ 2x = 0 and x = 6.

If x = 0 then from equation (2) y = x - 6

⇒ y = -6

If x = 6 then y = x - 6

⇒ y = 0

Therefore, the x-coordinates of the given system of equations are 0 and 6.

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What are the x-coordinates of the solutions to this system of equations?
x² + y² = 36, y = x - 6.

Summary:

The x-coordinates of the solutions to this system of equations x² + y² = 36, y = x - 6. are 0 and 6.