An illustration of a coordinate plane with four quadrants shows the x axis extending from negative 10 to 10 in increments of 1 and the y axis extending from negative 5 to 15 in increments of 1. A solid line and a dotted line with arrows at both ends intersect each other. The equation of the solid line is y equals one half x plus 6. The equation of the dotted line is y equals 2 x plus 3. The lines intersect at left parenthesis 2 comma 7 right parenthesis which is not plotted as a point.

Question

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)
left parenthesis 2 comma 7 right parenthesis

(7, 2)
left parenthesis 7 comma 2 right parenthesis

(−2, 7)
left parenthesis negative 2 comma 7 right parenthesis

(2,−7)

Answer 1

The solution to the system of equations is the point where the two lines intersect. Based on your description, the solid line given by the equation \( y = \frac{1}{2}x + 6 \) and the dotted line given by the equation \( y = 2x + 3 \) intersect at the point \( (2, 7) \).

Thus, the correct response is:

(2, 7)