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.
Estimate the solution to the system of these linear equations based on the graph.
y=2x+3
y=12x+6
(1 point)
Responses
(7, 2)
left parenthesis 7 comma 2 right parenthesis
(2, 7)
left parenthesis 2 comma 7 right parenthesis
(2,−7)
left parenthesis 2 comma negative 7 right parenthesis
(−2, 7)
left parenthesis negative 2 comma 7 right parenthesis
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1 answer
Based on the description provided, the solution to the system of equations \(y = 2x + 3\) and \(y = \frac{1}{2}x + 6\) is the point where the two lines intersect. According to your description, the lines intersect at the point \((2, 7)\).
Thus, the correct response is:
(2, 7)
