Question

Use the graph to the right to complete parts a through c below.
-4
-2
2
4
-2
2
4
6
x
y
(-2, 0)
(2, 2)



x y graph
Question content area bottom
Part 1
a. Describe the solution set for the system of equations that consists of the equation of the line shown and y equals one half x minus 3
.
A.
The solution set is
  
enter your response here. ​(Type an ordered​ pair.)
B.
There are infinitely many solutions.
C.
There is no solution.
Your answer is correct.
Part 2
b. Describe the solution set for the system of equations that consists of the equation of the line shown and 2 x plus y equals 6.
A.
The solution set is
  
left parenthesis 2 comma 2 right parenthesis. ​(Type an ordered​ pair.)
Your answer is correct.B.
There are infinitely many solutions.
C.
There is no solution.
Part 3
c. Describe the solution set for the system of equations that consists of the equation of the line shown and x minus 2 y equals negative 2.
A.
The solution set is
  
enter your response here. ​(Type an ordered​ pair.)
B.
There are infinitely many solutions.
C.
There is no solution.

Answer 1

From the graph the line is y = (1/2)x + 1 (it goes through (-2,0) and (2,2)).

a. y = (1/2)x − 3 has the same slope but different intercept, so the lines are parallel — there is no solution.

b. Solve 2x + y = 6 with y = (1/2)x + 1:
2x + (1/2)x + 1 = 6 -> (5/2)x = 5 -> x = 2, y = 2.
Solution: (2, 2).

c. x − 2y = −2 rearranges to y = (1/2)x + 1, which is the same line, so there are infinitely many solutions.