Estimate the solution to the system of these linear equations based on the graph. y=2x+3 y=12x+6 (1 point) Responses (2,7) open paren 2 comma 7 close paren (2,−7) open paren 2 comma negative 7 close paren (7,2) open paren 7 comma 2 close paren (−2,7 )

Answer 1

To solve the system of linear equations given by \(y = 2x + 3\) and \(y = 12x + 6\), you can find the point where the two lines intersect.

1. Set the equations equal to each other since they both equal \(y\): \[ 2x + 3 = 12x + 6 \]

2. Rearranging gives: \[ 3 - 6 = 12x - 2x \] \[ -3 = 10x \]

3. Solve for \(x\): \[ x = -\frac{3}{10} \]

4. Substitute \(x\) back into either equation to find \(y\): Using \(y = 2x + 3\): \[ y = 2(-\frac{3}{10}) + 3 = -\frac{6}{10} + 3 = 3 - 0.6 = 2.4 \]

So, the intersection point is \((-0.3, 2.4)\).

Now the given responses are:

• (2, 7)
• (2, -7)
• (7, 2)
• (-2, 7)

None of these points match the calculated intersection point exactly, but among the options, none corresponds to the solution derived from the equations. If you are estimating based on given graph options, you should select the point that looks closest based on visual estimation of the lines on a graph.

Without a visual, it's challenging to provide an accurate estimate. However, look for the point that seems closest to the expected value of around (-0.3, 2.4).