To estimate the solution to the system of linear equations based on the given graphs of the lines \( y = 2x + 3 \) and \( y = 12x + 6 \), we need to find the point where these two lines intersect.
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Find the intersection point by setting the equations equal to each other:
\[ 2x + 3 = 12x + 6 \]
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Solve for \( x \):
\[ 3 - 6 = 12x - 2x \] \[ -3 = 10x \] \[ x = -\frac{3}{10} = -0.3 \]
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Now substitute \( x = -0.3 \) back into one of the original equations to find \( y \). We'll use the first equation:
\[ y = 2(-0.3) + 3 \] \[ y = -0.6 + 3 = 2.4 \]
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Thus, the intersection point is approximately \( (-0.3, 2.4) \).
Given the response options provided:
- (2, 7)
- (2, −7)
- (7, 2)
- (−2, 7)
None of the options match directly with the calculated intersection point. However, the point that is close to this is (2, 7), considering graph estimation may not yield exact values.
But if we are strictly sticking to your provided options based on typical graph estimation, my best estimate might lean towards none being perfectly accurate, yet (2, 7) is the most plausible based on a general guess with varying graph lines.
However, if there was a graph to visually inspect, do refer back to where the lines intersect visually to assist the selection further.
1 answer