Answer:
The ordered pair (3,1/2) is not a common point, the statement is false
The solution is the point (0.667, 6.333) (common point)
Step-by-step explanation:
we have
[tex]y=2x+5[/tex] -----> equation A
[tex]y=\frac{1}{2}x+6[/tex] ----> equation B
we know that
If a ordered pair is a common point between the two lines,
then
the ordered pair must satisfy both equations
step 1
Verify if the ordered pair (3,1/2) satisfy equation A
substitute the value of x and the value of y in the equation A and then compare the results
For x=3, y=1/2
[tex]\frac{1}{2}=2(3)+5[/tex]
[tex]\frac{1}{2}=11[/tex] ----> is not true
The ordered pair don't satisfy the equation A
therefore
The ordered pair is not a common points both lines
The statement is false
step 2
Find the common point between the two lines
[tex]y=2x+5[/tex] -----> equation A
[tex]y=\frac{1}{2}x+6[/tex] ----> equation B
Solve the system of equations by graphing
The intersection point both graphs is the solution of the system (common point)
using a graphing tool
The solution is the point (0.667, 6.333) (common point)
see the attached figure
