Question

WILL MARK BRAINLEST
The graph shows two lines, A and B.
A graph is shown with x- and y-axes labeled from 0 to 6 at increments of 1. A straight line labeled A joins the ordered pair 0, 6 with the ordered pair 6, 3. Another straight line labeled B joins the ordered pair 0, 0 with the ordered pair 6, 6.
Part A: How many solutions does the pair of equations for lines A and B have? Explain your answer. (5 points)
Part B: What is the solution to the equations of lines A and B? Explain your answer. (5 points)

Answer 1

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)

Find the slope

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)

Find the slope

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

Answer 2

Answer:

Step-by-step explaPart 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)

Find the slope

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)

Find the slope

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

nation: