Question
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Solving Systems of Equations by Graphing Quick Check
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Question
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
(12,−1)
left parenthesis 12 comma negative 1 right parenthesis
(1,−12)
left parenthesis 1 comma negative 12 right parenthesis
(−1, 12)
left parenthesis negative 1 comma 12 right parenthesis
(−1,−12)
left parenthesis negative 1 comma negative 12 right parenthesis
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Solving Systems of Equations by Graphing Quick Check
5 of 55 of 5 Items
Question
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
(12,−1)
left parenthesis 12 comma negative 1 right parenthesis
(1,−12)
left parenthesis 1 comma negative 12 right parenthesis
(−1, 12)
left parenthesis negative 1 comma 12 right parenthesis
(−1,−12)
left parenthesis negative 1 comma negative 12 right parenthesis
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Answers
GPT-4o mini
To estimate the solution to the system of linear equations given in the problem, we need to identify the point of intersection of the two lines based on the descriptions provided.
The equations of the lines are:
1. Solid line: \( y = -2x + 10 \)
2. Dotted line: \( y = -5x + 7 \)
According to the information, the lines intersect at the point \( (-1, 12) \). This point is not plotted as a point on the graph because it is the intersection point of the two lines.
Among the response options provided:
- (12, -1)
- (1, -12)
- **(-1, 12)**
- (-1, -12)
The correct response is **(-1, 12)**, which is the estimated solution to the system of equations.
The equations of the lines are:
1. Solid line: \( y = -2x + 10 \)
2. Dotted line: \( y = -5x + 7 \)
According to the information, the lines intersect at the point \( (-1, 12) \). This point is not plotted as a point on the graph because it is the intersection point of the two lines.
Among the response options provided:
- (12, -1)
- (1, -12)
- **(-1, 12)**
- (-1, -12)
The correct response is **(-1, 12)**, which is the estimated solution to the system of equations.