Question
1. y=5x–4
2. y=–2x+3
3. y=3x+1
4. 2y=6x+2
5. y–5x=+2
6. y–4x+1=0
b. Graph all six equations on the coordinate grid and label them.
c. Circle the two equations that form a system with infinite solutions.
d. Put a square around the two equations that form a system with no solution.
e. Underline the two equations that form a system with one solution.
What do you notice about equations that are in each of these categories? Use
complete sentences to answer the questions that follow
2. y=–2x+3
3. y=3x+1
4. 2y=6x+2
5. y–5x=+2
6. y–4x+1=0
b. Graph all six equations on the coordinate grid and label them.
c. Circle the two equations that form a system with infinite solutions.
d. Put a square around the two equations that form a system with no solution.
e. Underline the two equations that form a system with one solution.
What do you notice about equations that are in each of these categories? Use
complete sentences to answer the questions that follow
Answers
GPT 3.5
To graph all six equations, we will choose x-values and solve for y. Then, we will plot the points on the coordinate grid.
1. y = 5x – 4
For x = 0, y = -4, giving us the point (0,-4).
For x = 1, y = 5(1) - 4 = 1, giving us the point (1,1).
Joining these points, we get the line:
2. y = -2x + 3
For x = 0, y = 3, giving us the point (0,3).
For x = 1, y = -2(1) + 3 = 1, giving us the point (1,1).
Joining these points, we get the line:
3. y = 3x + 1
For x = 0, y = 1, giving us the point (0,1).
For x = 1, y = 3(1) + 1 = 4, giving us the point (1,4).
Joining these points, we get the line:
4. 2y = 6x + 2
We can rearrange the equation to y = 3x + 1.
This equation is the same as equation 3 and represents the same line.
5. y - 5x = 2
Rearranging the equation, we get y = 5x + 2.
For x = 0, y = 2, giving us the point (0,2).
For x = 1, y = 5(1) + 2 = 7, giving us the point (1,7).
Joining these points, we get the line:
6. y - 4x + 1 = 0
Rearranging the equation, we get y = 4x - 1.
For x = 0, y = -1, giving us the point (0,-1).
For x = 1, y = 4(1) - 1 = 3, giving us the point (1,3).
Joining these points, we get the line:
c. The two equations that form a system with infinite solutions are:
- 3. y = 3x + 1
- 4. 2y = 6x + 2 (or y = 3x + 1, as they represent the same line)
d. The two equations that form a system with no solution are:
- 1. y = 5x – 4
- 2. y = -2x + 3
e. The two equations that form a system with one solution are:
- 5. y - 5x = 2
- 6. y - 4x + 1 = 0
Observation:
- Equations that form a system with infinite solutions are essentially the same line or have the same slope-intercept form.
- Equations that form a system with no solution have different slopes and do not intersect.
- Equations that form a system with one solution have different slopes and intersect at a single point.
1. y = 5x – 4
For x = 0, y = -4, giving us the point (0,-4).
For x = 1, y = 5(1) - 4 = 1, giving us the point (1,1).
Joining these points, we get the line:
2. y = -2x + 3
For x = 0, y = 3, giving us the point (0,3).
For x = 1, y = -2(1) + 3 = 1, giving us the point (1,1).
Joining these points, we get the line:
3. y = 3x + 1
For x = 0, y = 1, giving us the point (0,1).
For x = 1, y = 3(1) + 1 = 4, giving us the point (1,4).
Joining these points, we get the line:
4. 2y = 6x + 2
We can rearrange the equation to y = 3x + 1.
This equation is the same as equation 3 and represents the same line.
5. y - 5x = 2
Rearranging the equation, we get y = 5x + 2.
For x = 0, y = 2, giving us the point (0,2).
For x = 1, y = 5(1) + 2 = 7, giving us the point (1,7).
Joining these points, we get the line:
6. y - 4x + 1 = 0
Rearranging the equation, we get y = 4x - 1.
For x = 0, y = -1, giving us the point (0,-1).
For x = 1, y = 4(1) - 1 = 3, giving us the point (1,3).
Joining these points, we get the line:
c. The two equations that form a system with infinite solutions are:
- 3. y = 3x + 1
- 4. 2y = 6x + 2 (or y = 3x + 1, as they represent the same line)
d. The two equations that form a system with no solution are:
- 1. y = 5x – 4
- 2. y = -2x + 3
e. The two equations that form a system with one solution are:
- 5. y - 5x = 2
- 6. y - 4x + 1 = 0
Observation:
- Equations that form a system with infinite solutions are essentially the same line or have the same slope-intercept form.
- Equations that form a system with no solution have different slopes and do not intersect.
- Equations that form a system with one solution have different slopes and intersect at a single point.
NOMAN
what number should be on both sides of the equation -7x = 14 be divided by to solve for the value of x