SOLUTION: The coordinates below represent two linear equations. How many solutions does this system of equations have? Line 1 x y �6 3 3 6 Line 2 x y �3 1 3 3 A. 0

Question 934343: The coordinates below represent two linear equations.

How many solutions does this system of equations have?

Line 1
x y
�6 3
3 6
Line 2
x y
�3 1
3 3

A.
0

B.
exactly 1

C.
exactly 2

D.
infinitely many
Found 2 solutions by TimothyLamb, MathLover1:
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
line 1:
m = dy/dx
m = (6 - 3)/(3 + 6)
m = 3/9
m = 1/3
y - 6 = (1/3)(x - 3)
y = (1/3)x - 1 + 6
y = (1/3)x + 5
---
line 2:
m = dy/dx
m = (3 - 1)/(3 + 3)
m = 2/6
m = 1/3
y - 3 = (1/3)(x - 3)
y = (1/3)x - 1 + 3
y = (1/3)x + 2
---
the lines are parallel (equal slopes), but distinct (different y-intercepts) ...
the linear system has no solutions
---
answer:
A. 0
---
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Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
given:
Line 1
|
|
|
first find equation of a line passing through given points:

Solved by pluggable solver: Find the equation of line going through points

hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (-6, 3) and (x2, y2) = (3, 6).
Slope a is .
Intercept is found from equation , or . From that,
intercept b is , or .

y=(0.333333333333333)x + (5)

Your graph:

Line 2
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|
|

Solved by pluggable solver: Find the equation of line going through points

hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (-3, 1) and (x2, y2) = (3, 3).
Slope a is .
Intercept is found from equation , or . From that,
intercept b is , or .

y=(0.333333333333333)x + (2)

Your graph:

see both lines on a graph:

From the graph, we can see that the two lines are parallel and will never intersect. So there are no solutions and the system is inconsistent.
according to Euclidean geometry, if two lines are distinct but have the same slope they are said to be parallel and have points in common.
so, your answer is A.
It is also good to know that, according to non-Euclidean geometry (so called projective geometry) any pair of lines at some point, but parallel lines do not intersect in the real plane. The line at infinity is added to the real plane. This completes the plane, because now intersect at a point which lies on the line at . Also, if any pair of lines intersects at a point on the line at infinity, then the pair of lines is parallel.
but we will keep A. as an answer to your question

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