# What are the x-coordinates of the solutions to this system of equations?

x^{2} + y^{2} = 36, y = x - 6.

**Solution:**

Given system of equations are

x^{2} + y^{2 }= 36 --- (1)

y = x - 6 --- (2)

Replace y from equation 2 in equation 1,

⇒ x^{2} + (x - 6)^{2} = 36

Expanding (x - 6)^{2} using (a - b)^{2} = a^{2} + b^{2} - 2ab

⇒ x^{2} + x^{2} - 12x + 36 = 36

⇒ 2x^{2} - 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.

## What are the x-coordinates of the solutions to this system of equations?

x^{2} + y^{2} = 36, y = x - 6.

**Summary:**

The x-coordinates of the solutions to this system of equations x^{2} + y^{2} = 36, y = x - 6. are 0 and 6.

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