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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
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.
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.
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