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Answer:
Part A) The system has one solution
Part B) The solution is the point (4,4)
Step-by-step explanation:
step 1
Find the equation of the line A
we have
(0,6) and (6,3)
<em>Find the slope</em>
m=(3-6)/(6-0)
m=-0.5
Find the equation of the line into slope intercept form
y=mx+b
we have
m=-0.5
b=6 -----> the point (0,6) is the y-intercept
substitute
y=-0.5x+6 ------> equation A
step 2
Find the equation of the line B
we have
(0,0) and (6,6)
<em>Find the slope</em>
m=(6-0)/(6-0)
m=1
Find the equation of the line into slope intercept form
y=mx+b
we have
m=1
b=0 -----> the line represent a direct variation
substitute
y=x ------> equation B
step 3
Find how many solutions does the pair of equations for lines A and B have
we have
y=-0.5x+6 ------> equation A
y=x ------> equation B
Solve the system of equations by graphing
Remember that the solution of the system of equations is the intersection point both lines
using a graphing tool
There is one point of intersection
therefore
The system has one solution
see the attached figure
step 4
What is the solution to the equations of lines A and B?
we know that
The solution of the system of equations is the intersection point both lines
The intersection point is (4,4)
therefore
The solution is the point (4,4)
so
x=4,y=4
