Solving Systems of Equations by Graphing Quick Check
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Question
Use the image to answer the question.
A coordinate plane with four quadrants shows the x-axis ranging from negative 5 to 15 in increments of 1 and the y-axis ranging from negative 10 to 10 in increments of 1. A solid line and a dotted line intersect each other. The equation of the solid line is 2 x plus y equals 15. The equation of the dotted line is y equals negative x plus 5. The intersection of both lines is shown at positive 10 on the x-axis and negative 5 on the y-axis in quadrant 4.
Find the coordinates of the intersection point that solves the system of these two linear equations in two variables: 2x+y=15 and y=−x+5 .
(1 point)
Responses
(5,−10)
left parenthesis 5 comma negative 10 right parenthesis
(−10, 5)
left parenthesis negative 10 comma 5 right parenthesis
(−5, 10)
left parenthesis negative 5 comma 10 right parenthesis
(10,−5)
left parenthesis 10 comma negative 5 right parenthesis
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9 answers
Responses
No, because the graphs don’t intersect at (−2, 6).
No, because the graphs don’t intersect at left parenthesis negative 2 comma 6 right parenthesis .
Yes, because the graphs intersect at (−2, 6).
Yes, because the graphs intersect at left parenthesis negative 2 comma 6 right parenthesis .
No, because the graphs intersect at (−2, 6).
No, because the graphs intersect at left parenthesis negative 2 comma 6 right parenthesis .
Yes, because the graphs don’t intersect at (−2, 6).
An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 10 to 10 in increments of 1. A solid line and a dotted line with arrows at both the ends intersect each other. The equation of the solid line is y equals 5 x plus 10. The equation of the dotted line is y equals negative 2 x plus 3. The lines intersect at left parenthesis negative 1 comma 5 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+10
y=−2x+3
(1 point)
Responses
(5,−1)
left parenthesis 5 comma negative 1 right parenthesis
(1, 5)
left parenthesis 1 comma 5 right parenthesis
(−1, 5)
left parenthesis negative 1 comma 5 right parenthesis
(−1,−5)
left parenthesis negative 1 comma negative 5 right parenthesis
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Responses
Check the answer.
Check the answer.
Make a table of solutions of the linear equations.
Make a table of solutions of the linear equations.
Estimate the intersection point.
Estimate the intersection point.
Graph the lines.
Graph the lines.
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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2 answers