Question

The common point between lines y = 2x + 5 and y = ½ x + 6 is (3, 1/2).

Answer 1

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)

Explanation:

we have

`y=2x+5` -----> equation A

`y=(1)/(2)x+6` ----> 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

`(1)/(2)=2(3)+5`

`(1)/(2)=11` ----> 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

`y=2x+5` -----> equation A

`y=(1)/(2)x+6` ----> 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