Graph the systems of equations. {2x+y=8−x+2y=6
2 answers:
Answer:
Given system of equations are :
1). 2x + y = 8
2). -x + 2y = 6
Finding the intercepts of the equation (1) :
2x + y = 8
when x = 0 the y = 8
when y = 0 then x = 4
points are : (0,8) and (4,0)
Finding the intercepts of the equation (2) :
-x + 2y = 6
when x = 0 the y = 3
when y = 0 then x = -6
points are : (0,3) and (-6,0)
Hence, the required graphs of the given system of equation is attached below :
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g(x) = 2x -20
The x-intercept of this line is at x=10.
0 = 2x -20 . . . . the x-intercept is where g(x) = 0
20 = 2x
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The circle also intersects the x-axis at x=10, so that will be one point that is shared by the circle and g(x). A graph shows there is also another point of intersection, (6, -8).
Yes, the linear function g(x) will intersect the circle at 2 points with positive x-coordinates.
(change in y)/(change in x) = (-18 -(-20))/(1 - 0) = 2
so can be written in slope-intercept form as
g(x) = 2x -20
The x-intercept of this line is at x=10.
0 = 2x -20 . . . . the x-intercept is where g(x) = 0
20 = 2x
10 = x
The circle also intersects the x-axis at x=10, so that will be one point that is shared by the circle and g(x). A graph shows there is also another point of intersection, (6, -8).
Yes, the linear function g(x) will intersect the circle at 2 points with positive x-coordinates.