Math question please!!?

Question

What is the total number of points of intersection of the graphs of the
equations x2 + y2 = 16 and y = x?
(1) 1 (3) 3
(2) 2 (4) 4
tell me the specific steps
thanks

Answer 1

ok, you can substitute one equation into the other.

since y = x , then

x^2 + y^2 = 16 is equal to
x^2 + x^2 = 16 , thus adding like terms gives us
2x^2 = 16 divide by 2 both sides
x^2 = 8 take the square root of both sides
x = +/- sqrt (8)

ok, so now we know that they meet at x = +/- sqrt (8), lets find the y value

pick either equation, for simplicity y = x

y = +/- sqrt (8)

to verify the answer lets use the other equation to verify the answer

x^2 + y^2 = 16
x^2 + x^2 = 16
2x^2 = 16
2[+/-sqrt(8)]^2 = 16
2(8) = 16

so there are four intercept points:

y = +/- sqrt (8)
x = +/- sqrt (8)

cheers

Answer 2

x² + y² = 16 is a circle, radius 4, center at the origin. y = x is a line, slope = 1, y intercept = 0, so it passes through the origin. A line that goes through the center of a circle intersects the circle at 2 points.

To find those points, use y = x to replace y in the 1st equation:

x² + x² = 16
2x² = 16
x² = 8
x = ±√8 = ±2√2

and since y = x, the points of intersection are
(2√2,2√2) and (-2√2,-2√2)

Answer 3

Answer: (4)

since y = x , then

x² + y² = 16 is equal to
---> x² + x² = 16
2x² = 16
x² = 16/2 = 8
x = +/- sqrt (8)

and as mentioned before, y = x
therefore y = +/- sqrt (8) too

so there are four (4) intercept points:

y = +/- sqrt (8)
x = +/- sqrt (8)

Answer 4

note that the first expression is the equation of a circle centered at (0,0) or the origin. So you will have 2 intercepts in the x axis and two in the y axis.

the second equation is the equation of the line passing thru the origin. So the point (0,0) is the intercept.