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
  
enter your response here. ​(Type an ordered​ pair.)
B.
There are infinitely many solutions.
C.
There is no solution.

Answer 1

The line through (-2,0) and (2,2) has equation y = (1/2)x + 1.

a. y = (1/2)x − 3 is parallel (same slope 1/2) but different intercept, so no solution.

b. Substitute y = (1/2)x + 1 into 2x + y = 6:
2x + (1/2)x + 1 = 6 → (5/2)x = 5 → x = 2, y = 2.
Solution: (2, 2).