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)

(2, 7)
please

Answer 1

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.