6. a. Name a pair of equations that have exactly one point of intersection. How do you know?
1 answer:
Answer:
A system of linear equations will have exactly one point of intersection, for example:
2x+y=5
-x+y=2
However, a system of linear equations with no solution will have no points of intersection, for example:
-4x+10y=6
2x-5y=3
Sorry about c. though I'm confused on how a pair of equations can have infinite points of intersection unless x or y equals all real numbers which could happen if x or y both equaled all real numbers maybe
And the point of interesection for the system of equations in the problem you attached as an image is (2,-1)
I attached a photo below, and one of how to graph it
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Answer:
Step-by-step explanation:
a coordinate point is (x, y) so for point W (4, -1), 4 is the x-coordinate and -1 is the y-coordinate.
Start at the origin (O). Go 4 units to the right (along the x-axis in a positive direction) and then 1 unit down (in the y plane in a negative direction).
Answer:
y=3x-5
Step-by-step explanation:
First find the slope, 4+2 over 3-1, giving you the slope of three
then set up your equation, y=3x+?
I played with the y=3x - part on the website desmos graphing calculator, I first inserted the points then found the slope and then played with the equation till it went through both the points.
Answer:
mid point of AB (0.5 , 0)
Step-by-step explanation:
2x + 5y = 1 2x = 1 - 5y
y = 2xy+ 5 = (1 - 5y)*y + 5 = y - 5y² + 5
y-y = y - 5y² + 5 - y = - 5y² + 5
0 = - 5y² + 5
5y² = 5
y² = 1
y = 1 or y = -1
if y = 1 x = 1/2 (1 - 5) = -2 .... point A (-2 , 1)
if y = -1 x = 1/2 (1 + 5) = 3 ..... point B (3 , -1)
mid point of AB (x' , y') : x' = 1/2 (x₁ + x₂) = 1/2 (-2 + 3) = 1/2
y' = 1/2 (y₁ + y₂) = 1/2 (-1 + 1) = 0
