To estimate the solution to the system of linear equations given by \(y = 2x + 3\) and \(y = 12x + 6\), we can find the point where these two lines intersect.
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Set the equations equal to each other: \[ 2x + 3 = 12x + 6 \]
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Rearrange the equation: \[ 3 - 6 = 12x - 2x \implies -3 = 10x \implies x = -\frac{3}{10} \]
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Substitute \(x = -\frac{3}{10}\) back into either equation to find \(y\). Using the first equation: \[ y = 2\left(-\frac{3}{10}\right) + 3 = -\frac{6}{10} + 3 = 3 - 0.6 = 2.4 \]
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Thus, the intersection point is: \[ \left(-\frac{3}{10}, 2.4\right) \approx (-0.3, 2.4) \]
Now, looking at the answer choices:
- (7, 2)
- (2, -7)
- (−2, 7)
- (2, 7)
None of these points match the approximate solution of \((-0.3, 2.4)\). If you have a graph, please verify the intersection point visually or provide further details about the graph. Based on the calculations, the intersection points of the lines suggest they do not intersect at any of the given choices.