Question
Solve the following system of linear equations by graphing. Choose the answer that matches the solution.
y = 5x + 3
y = 5x + 15
answers:
No solutions
(3 , 5)
(5 , 3)
Infinite solutions
y = 5x + 3
y = 5x + 15
answers:
No solutions
(3 , 5)
(5 , 3)
Infinite solutions
Answers
Answer
you sure
Answered by
GPT-4o mini
To solve the system of linear equations by graphing, we need to analyze the two equations:
1. \( y = 5x + 3 \)
2. \( y = 5x + 15 \)
Both equations are in slope-intercept form (y = mx + b), where the slope (m) is 5 for both lines. However, the y-intercepts (b) are different:
- The first line has a y-intercept of 3.
- The second line has a y-intercept of 15.
This means that both lines have the same slope but different y-intercepts, indicating that they are parallel lines.
When graphing, parallel lines will never intersect. Therefore, there are no points (x, y) that satisfy both equations simultaneously.
Thus, the correct answer is:
**No solutions**
1. \( y = 5x + 3 \)
2. \( y = 5x + 15 \)
Both equations are in slope-intercept form (y = mx + b), where the slope (m) is 5 for both lines. However, the y-intercepts (b) are different:
- The first line has a y-intercept of 3.
- The second line has a y-intercept of 15.
This means that both lines have the same slope but different y-intercepts, indicating that they are parallel lines.
When graphing, parallel lines will never intersect. Therefore, there are no points (x, y) that satisfy both equations simultaneously.
Thus, the correct answer is:
**No solutions**
Answered by
GPT-4o mini
Yes, I am sure. Let's revisit the setup step by step to reinforce the conclusion:
1. **Identifying the equations**:
- Equation 1: \( y = 5x + 3 \) (this line has a slope of 5 and a y-intercept of 3)
- Equation 2: \( y = 5x + 15 \) (this line also has a slope of 5 but a different y-intercept of 15)
2. **Understanding the slopes**:
- Both lines have the same slope (5), which means they rise at the same angle.
3. **Understanding the intercepts**:
- The difference in y-intercepts (3 and 15) indicates that the two lines are parallel, meaning they will never cross or intersect at any point.
4. **Conclusion**:
- Since the lines are parallel, there is no solution that satisfies both equations simultaneously.
The final conclusion remains that there are **No solutions** to this system of equations, as they represent two distinct parallel lines in a graph.
1. **Identifying the equations**:
- Equation 1: \( y = 5x + 3 \) (this line has a slope of 5 and a y-intercept of 3)
- Equation 2: \( y = 5x + 15 \) (this line also has a slope of 5 but a different y-intercept of 15)
2. **Understanding the slopes**:
- Both lines have the same slope (5), which means they rise at the same angle.
3. **Understanding the intercepts**:
- The difference in y-intercepts (3 and 15) indicates that the two lines are parallel, meaning they will never cross or intersect at any point.
4. **Conclusion**:
- Since the lines are parallel, there is no solution that satisfies both equations simultaneously.
The final conclusion remains that there are **No solutions** to this system of equations, as they represent two distinct parallel lines in a graph.
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