Does the equation x2 - 10x + y2-6y = -30 intersect the x-axis?
A) Yes, because the center is a (5.3) and the radius is 4.
B) Yes, because the center is a (5.3) and the radius is 2.
C) Yes, because the center is a (-5, -3) and the radius is 2.
D) No, because the circle is entirely in the first quadrant.

D

Step-by-step explanation:

The correct answer is: No, because the circle is entirely in the first quadrant.

First, write the equation in standard form by completing the square.

x2 - 10x + y2 - 6y = -30

x2 - 10x + 25 + y2 - 6y + 9 = -30 + 25 + 9

(x - 5)2 + (y - 3)2 = 4

The circle is centered at (5, 3) with a radius of 2. Since 5 - 2 = 3 and 3 - 2 = 1, the circle is entirely in quadrant one and doesn't intersect the x-axis or y-axis.

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,

yes they are the same