To find the solution to the system of equations given by \(y = 2x + 3\) and \(y = 12x + 6\), we can determine their intersection point.
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Set the equations equal to each other:
\[ 2x + 3 = 12x + 6 \]
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Rearranging gives:
\[ 3 - 6 = 12x - 2x \] \[ -3 = 10x \]
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Solve for \(x\):
\[ x = -\frac{3}{10} = -0.3 \]
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Substitute \(x = -0.3\) back into either equation to find \(y\). We'll use \(y = 2x + 3\):
\[ y = 2(-0.3) + 3 = -0.6 + 3 = 2.4 \]
Thus, the intersection point is approximately \((-0.3, 2.4)\).
Now, looking at the provided responses:
- (2,7)
- (2,−7)
- (7,2)
- (−2,7)
None of these points match \((-0.3, 2.4)\) exactly. However, we can hint that since all points have integers and our calculation shows it is between \(-0.3\) and \(0\) for \(x\), and \(2.4\) is closer to \(2\) than to \(7\).
If we were to select the best guess from the options, based on a graph interpretation (trying visual approximation rather than exact calculations, but yet suggesting checked pairs seem viable):
- \( (2, 7)\) or \( (−2, 7)\) would be further from \(y\)
- The closest to our approximate intersection produces reliable values.
In summary, the calculated intersection does not exactly align with the answer choices provided based on the graphical approach without visual data. The best estimate based on mathematical calculation, which is unseen since it requires interpretation of the graph, suggests approximate interference or nearby values.
1 answer