Duplicate Question
The question on this page has been marked as a duplicate question.
Original Question
Estimate the solution to the system of these linear equations based on the graph. y=2x+3 y=12x+6 (1 point) (7, 2) (2,−7) (−2, 7...Asked by bruh no
Estimate the solution to the system of these linear equations based on the graph.
y=2x+3
y=12x+6 (1 point)
(7, 2)
(2,−7)
(−2, 7)
(2, 7)
please
y=2x+3
y=12x+6 (1 point)
(7, 2)
(2,−7)
(−2, 7)
(2, 7)
please
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To estimate the solution to the system of equations given the lines in the equations \(y = 2x + 3\) and \(y = 12x + 6\), we should find the point where these two lines intersect.
1. Let's first express both equations in standard form.
- For the first equation, \(y = 2x + 3\):
\[ 2x - y + 3 = 0 \]
- For the second equation, \(y = 12x + 6\):
\[ 12x - y + 6 = 0 \]
2. Next, let's set the equations equal to each other to find the intersection point:
\[ 2x + 3 = 12x + 6 \]
3. Rearranging this gives:
\[ 2x - 12x + 3 - 6 = 0 \]
\[ -10x - 3 = 0 \]
\[ -10x = 3 \]
\[ x = -\frac{3}{10} \]
4. Substitute \(x = -\frac{3}{10}\) back into either of the original equations to find \(y\):
\[
y = 2\left(-\frac{3}{10}\right) + 3 = -\frac{6}{10} + 3 = 3 - 0.6 = 2.4
\]
So the intersection point is approximately \((-0.3, 2.4)\).
Now, let's evaluate the provided choices to see if any of them match this estimated point:
1. (7, 2)
2. (2, -7)
3. (-2, 7)
4. (2, 7)
None of these options match \((-0.3, 2.4)\) closely. However, if we were to consider rounding or estimating based on visual observation from a graph, you might have to choose the one that seems closest based on other observations, but none numerically match the intersection point when calculated.
If you have a graph of these equations available, looking for the estimated point visually would help indicate which of the listed points is nearest to where the lines intersect.
1. Let's first express both equations in standard form.
- For the first equation, \(y = 2x + 3\):
\[ 2x - y + 3 = 0 \]
- For the second equation, \(y = 12x + 6\):
\[ 12x - y + 6 = 0 \]
2. Next, let's set the equations equal to each other to find the intersection point:
\[ 2x + 3 = 12x + 6 \]
3. Rearranging this gives:
\[ 2x - 12x + 3 - 6 = 0 \]
\[ -10x - 3 = 0 \]
\[ -10x = 3 \]
\[ x = -\frac{3}{10} \]
4. Substitute \(x = -\frac{3}{10}\) back into either of the original equations to find \(y\):
\[
y = 2\left(-\frac{3}{10}\right) + 3 = -\frac{6}{10} + 3 = 3 - 0.6 = 2.4
\]
So the intersection point is approximately \((-0.3, 2.4)\).
Now, let's evaluate the provided choices to see if any of them match this estimated point:
1. (7, 2)
2. (2, -7)
3. (-2, 7)
4. (2, 7)
None of these options match \((-0.3, 2.4)\) closely. However, if we were to consider rounding or estimating based on visual observation from a graph, you might have to choose the one that seems closest based on other observations, but none numerically match the intersection point when calculated.
If you have a graph of these equations available, looking for the estimated point visually would help indicate which of the listed points is nearest to where the lines intersect.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.