Use the image to answer the question.
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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From the graph, it appears that the lines intersect at a point with x-coordinate of approximately -1 and y-coordinate of approximately 12. Therefore, the estimate for the solution to the system of linear equations is (-1, 12).
The estimate for the solution to the system of linear equations based on the graph is (-1, 12), or in proper notation, (−1, 12).
To estimate the solution to the system of linear equations based on the graph, we need to find the point where the solid line and the dotted line intersect.
From the given equations, we know that the solid line represents the equation y = -2x + 10 and the dotted line represents the equation y = -5x + 7.
To find the point of intersection, we need to solve these two equations simultaneously.
Setting the right-hand sides of the equations equal to each other, we have:
-2x + 10 = -5x + 7
Simplifying, we get:
3x = 3
Dividing both sides by 3, we find:
x = 1
Now, substituting this value of x back into either of the original equations, let's use the solid line equation:
y = -2(1) + 10
Simplifying, we get:
y = 8
Therefore, the estimated solution to the system of linear equations based on the graph is (1, 8).
Since the question states that the actual point of intersection is (-1, 12), this means that our estimate is not correct.