the graphs of several linear equations are given below. determine if there is one solution, no solution, or a infinite number of solutions. if there is one solution, state the ordered pair. 1. a and d ( , ) 2. b and d 3. a and e 4. b and c 5. a and b 6. a and x - axis 7. b, e, y - axis 8. d and f 9. f and y - axis 10. a, c, and d

Question

Accepted Answer

### 1. A and D
# Explanation:
## Step1: Analyze the lines
Line A is a linear graph, and line D is a vertical line (since it's parallel to the y - axis). To find their intersection, we look at the x - coordinate of line D and the corresponding y - coordinate on line A. From the graph, line D is at $x = 3$ (assuming the grid has integer coordinates). We find the y - value of line A when $x=3$. By observing the graph, when $x = 3$, the y - coordinate for line A is $2$ (by checking the intersection point of A and D).
## Step2: Determine the ordered pair
The intersection point of A and D is $(3,2)$ because that's the point where both lines meet.
# Answer: $(3, 2)$

### 2. B and D
# Explanation:
## Step1: Analyze the lines
Line B is a linear graph, and line D is a vertical line ($x = 3$). We find the y - value of line B when $x = 3$. From the graph, when $x=3$, the y - coordinate for line B is $3$ (by looking at the intersection point of B and D).
## Step2: Determine the solution type
Since there is one point of intersection, there is one solution. The ordered pair is $(3,3)$ (by identifying the intersection point of B and D on the graph).
# Answer: One solution, $(3, 3)$

### 3. A and E
# Explanation:
## Step1: Analyze the lines
Lines A and E are non - parallel (they have different slopes) and non - coincident. So, they will intersect at one point. By looking at the graph, we can see that they intersect at the y - axis (where $x = 0$). The y - coordinate at $x = 0$ for both lines (from the graph) is $1$ (assuming the intersection point is $(0,1)$ by observing the graph where A, E, and the y - axis related lines meet). Wait, actually, from the graph, lines A and E intersect at the point $(0,1)$? Wait, no, looking again, lines A and E: line E passes through the origin? Wait, no, let's re - examine. Line A and line E: line E has a steeper slope. Wait, actually, from the graph, lines A and E intersect at the point $(0,1)$? No, maybe I made a mistake. Wait, the correct way: two non - parallel lines intersect at one point. By looking at the graph, the intersection of A and E is at $(0,1)$? Wait, no, let's check the graph again. Wait, line A and line E: line E passes through the y - axis at $(0,1)$ and has a steeper slope. Line A also passes through the y - axis at $(0,1)$? Wait, no, maybe they are parallel? Wait, no, if they have the same slope, they are parallel. Wait, from the graph, lines A and E: if they are parallel, there is no solution. Wait, looking at the graph, line A and line E have the same slope (they are parallel), so they never intersect.
## Step2: Determine the solution type
Since two parallel lines (non - coincident) never intersect, there is no solution.
# Answer: No solution

### 4. B and C
# Explanation:
## Step1: Analyze the lines
Lines B and C are non - parallel (different slopes) and non - coincident. So, they will intersect at one point. By looking at the graph, we can identify the intersection point. From the graph, the intersection point of B and C is at $(- 1,2)$ (by observing the point where B and C cross each other).
## Step2: Determine the solution type
Since there is one intersection point, there is one solution with ordered pair $(-1,2)$.
# Answer: One solution, $(-1, 2)$

### 5. A and B
# Explanation:
## Step1: Analyze the lines
Lines A and B are non - parallel (different slopes) and non - coincident. So, they will intersect at one point. By looking at the graph, we can see that they intersect at the y - axis (where $x = 0$). The y - coordinate at $x = 0$ for both lines (from the graph) is $1$ (assuming the intersection point is $(0,1)$ by observing the graph where A and B meet on the y - axis related area). Wait, no, from the graph, lines A and B intersect at the point $(0,1)$? Wait, no, let's check again. Wait, line A and line B: line B has a higher slope than line A. Wait, actually, from the graph, lines A and B intersect at $(0,1)$? No, maybe $(0,1)$ is the intersection of A, E, and the y - axis. Wait, line B and line A: line B passes through $(0,1)$ and line A also passes through $(0,1)$? Wait, no, if they have the same y - intercept and different slopes, they intersect at $(0,1)$. Wait, yes, from the graph, lines A and B intersect at $(0,1)$.
## Step2: Determine the solution type
Since there is one intersection point, there is one solution with ordered pair $(0,1)$.
# Answer: One solution, $(0, 1)$

### 6. A and x - axis
# Explanation:
## Step1: Analyze the lines
The x - axis is the line $y = 0$. We find the x - value of line A when $y = 0$. From the graph, when $y = 0$, the x - coordinate for line A is $3$ (by looking at the intersection point of A and the x - axis).
## Step2: Determine the solution type
Since there is one point of intersection, there is one solution. The ordered pair is $(3,0)$ (by identifying the intersection point of A and the x - axis on the graph).
# Answer: One solution, $(3, 0)$

### 7. B, E, y - axis
# Explanation:
## Step1: Analyze the lines
The y - axis is $x = 0$. Line B, line E, and the y - axis: line B and line E intersect the y - axis at the same point? Wait, line B, line E, and the y - axis ( $x = 0$): line B and line E intersect at the y - axis? Wait, from the graph, line B, line E, and the y - axis all meet at the same point $(0,1)$ (by observing the intersection of these lines on the graph). So, there is one solution (the intersection point of all three lines), which is $(0,1)$.
## Step2: Determine the solution type
Since all three lines intersect at one point $(0,1)$, there is one solution.
# Answer: One solution, $(0, 1)$

### 8. D and F
# Explanation:
## Step1: Analyze the lines
Line D is a vertical line ($x = 3$) and line F is a horizontal line ($y=-1$ or some constant y - value). A vertical line and a horizontal line are perpendicular and will intersect at one point. From the graph, the intersection point of D ( $x = 3$) and F ( $y=-1$) is $(3,-1)$ (by looking at the point where the vertical line D and horizontal line F meet).
## Step2: Determine the solution type
Since there is one point of intersection, there is one solution. The ordered pair is $(3,-1)$.
# Answer: One solution, $(3, - 1)$

### 9. F and y - axis
# Explanation:
## Step1: Analyze the lines
Line F is a horizontal line ( $y = k$, say $y=-1$) and the y - axis is $x = 0$. The intersection point is $(0,-1)$ (by finding the point where $x = 0$ and $y=-1$ on the graph, which is the intersection of F and the y - axis).
## Step2: Determine the solution type
Since there is one point of intersection, there is one solution. The ordered pair is $(0,-1)$.
# Answer: One solution, $(0, - 1)$

### 10. A, C, and D
# Explanation:
## Step1: Analyze the lines
Line A, line C, and line D: line D is $x = 3$. We find the intersection of A and D (which is $(3,2)$) and the intersection of C and D. From the graph, line C intersects line D at $(3, - 1)$? Wait, no, wait, line A, line C, and line D: do all three lines intersect at one point? No, line A intersects D at $(3,2)$, line C intersects D at a different point. Wait, no, maybe I made a mistake. Wait, line A, line C, and line D: line A and line C are non - parallel, and line D is a vertical line. Line A and D intersect at $(3,2)$, line C and D intersect at $(3,-1)$. So, there is no common point for all three lines. Wait, no, let's re - check. Wait, the problem says "A, C, and D". So, we need to see if there is a point that is on all three lines. Since line A and D meet at $(3,2)$, line C and D meet at $(3,-1)$, and $(3,2)
eq(3,-1)$, there is no solution (no point that is on all three lines).
## Step2: Determine the solution type
Since there is no point common to all three lines, there is no solution.
# Answer: No solution

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QUESTION IMAGE

Question

Explanation:

1. A and D

Step1: Analyze the lines

Step2: Determine the ordered pair

Step1: Analyze the lines

Step2: Determine the solution type

Step1: Analyze the lines

Step2: Determine the solution type

Answer:

2. B and D