SOLUTION: The coordinates below represent two linear equations. The coordinates below represent two linear equations. How many solutions does this system of equations have? Line

Algebra ->  Linear-equations -> SOLUTION: The coordinates below represent two linear equations. The coordinates below represent two linear equations. How many solutions does this system of equations have? Line       Log On


   

Question 953239: The coordinates below represent two linear equations.
The coordinates below represent two linear equations.

How many solutions does this system of equations have?

Line 1
x y
3 5
0 4
Line 2
x y
0 4
6 2


A.
0

B.
exactly 1

C.
exactly 2

D.
infinitely many
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Line 1
x| y
3|%095
0|%094
first find the equation of the line using given points:
y=mx%2Bb......0|%094
4=m%2A0%2Bb
b=4
y=mx%2Bb......3|%095
5=m%2A3%2B4
5-4=3m
m=1%2F3
so, equation is:y=%281%2F3%29x%2B4

Line 2
x|%09y
0|%094
6|%092

y=mx%2Bb......0|%094
4=m%2A0%2Bb
b=4
y=mx%2Bb......6|%092
6=m%2A2%2B4
6-4=2m
m=2%2F2
m=1
so, equation is:y=x%2B4
y=%281%2F3%29x%2B4
y=x%2B4
------------------if left sides equal, then right sides equal too
%281%2F3%29x%2B4=x%2B4..........solve for x
x%2F3=x%2B4-4
x-x%2F3=0
2x%2F3=0
highlight%28x=0%29
then y=0%2B4=>highlight%28y=4%29
answer is:this system of equations have
B.
exactly 1 solution
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%2B4%2C+%281%2F3%29x%2B4%29+