To estimate the solution to the system of equations given by \( y = 2x + 3 \) and \( y = 12x + 6 \), we can find the point of intersection of these two lines.
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Set the equations equal to each other:
\( 2x + 3 = 12x + 6 \) -
Rearranging the equation:
\[ 2x + 3 - 6 = 12x \]
\[ 2x - 12x = 6 - 3 \]
\[ -10x = 3 \]
\[ x = -\frac{3}{10} \] -
Substituting \( x \) back into one of the original equations to find \( y \):
Using \( y = 2x + 3 \):
\[ y = 2\left(-\frac{3}{10}\right) + 3 \]
\[ y = -\frac{6}{10} + 3 \]
\[ y = -0.6 + 3 \]
\[ y = 2.4 \]
So the intersection point is approximately \( (-0.3, 2.4) \).
Now, let's look at the provided options:
- (2, 7)
- (2, −7)
- (7, 2)
- (−2, 7)
None of these points match our estimated intersection point directly. However, if we plot both equations, we would observe that the solution, which is the point of intersection, is around \((-0.3, 2.4)\), which is not close to any given options directly.
Since we are asked to estimate based on a graph and the only point nearby that has reasonable values would be \((-2, 7)\), but it is still not the correct intersection; hence, visual confirmation or an updated graphical method might give better options, if possible.
Do ensure you check the graph provided, as it could have further insight into which of those points could be the closest approximation in terms of vertical or horizontal line intersection views.