An illustration of a coordinate plane with four quadrants shows a solid line and a dotted line with arrows at both the ends intersecting with each other. The x axis extends from negative 10 to 10 in increments of 1. The y axis extends from negative 5 to 15 in increments of 1. The equation of the solid line is y equals negative 2 x plus 10. The equation of the dotted line is y equals negative 5 x plus 7. The lines intersect at left parenthesis negative 1 comma 12 right parenthesis which is not plotted as a point.
Estimate the solution to the system of these linear equations based on the graph.
y=−5x+7
y=−2x+10
(1 point)
Responses
(−1, 12)
left parenthesis negative 1 comma 12 right parenthesis
(12,−1)
left parenthesis 12 comma negative 1 right parenthesis
(−1,−12)
left parenthesis negative 1 comma negative 12 right parenthesis
(1,−12)
left parenthesis 1 comma negative 12 right parenthesis
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1 answer
The solution to the system of equations represented by the lines is the point at which they intersect. According to your description, the solid line (represented by the equation \(y = -2x + 10\)) and the dotted line (represented by the equation \(y = -5x + 7\)) intersect at the point \((-1, 12)\).
Therefore, the correct response is:
(-1, 12)
