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
(−10, 5)
left parenthesis negative 10 comma 5 right parenthesis
(−5, 10)
left parenthesis negative 5 comma 10 right parenthesis
(5,−10)
left parenthesis 5 comma negative 10 right parenthesis
(10,−5)
left parenthesis 10 comma negative 5 right parenthesis
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The coordinates of the intersection point are (10, -5).
Is (−2, 6) a solution to the system of these linear equations: x+2y=10 and 3x+y=0? Why?(1 point)
Responses
Yes, because the graphs don’t intersect at (−2, 6).
Yes, 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 .
No, because the graphs don’t intersect at (−2, 6).
No, because the graphs intersect at (-2, 6).
Solving Systems of Equations by Graphing Quick Check
3 of 53 of 5 Items
Question
Use the image to answer the question.
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
(−1, 5)
left parenthesis negative 1 comma 5 right parenthesis
(−1,−5)
left parenthesis negative 1 comma negative 5 right parenthesis
(1, 5)
left parenthesis 1 comma 5 right parenthesis
(5,−1)
left parenthesis 5 comma negative 1 right parenthesis
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Based on the graph, the estimated solution to the system of these linear equations is (-1, 5).
What is the last step to solving a system of equations?(1 point)
Responses
Check the answer.
Check the answer.
Estimate the intersection point.
Estimate the intersection point.
Make a table of solutions of the linear equations.
Make a table of solutions of the linear equations.
Graph the lines.
Graph the lines.
The last step to solving a system of equations is to check the answer.
Use the image to answer the question.
A solid line and a dotted line intersect on a coordinate plane. The point of intersection is plotted. The values on the x-axis range from 0 to 100 in increments of 5. The values on the y-axis range from 0 to 60 in increments of 5. Both lines slope downward from left to right. The solid line passes through left parenthesis 45 comma 60 right parenthesis, left parenthesis 60 comma 40 right parenthesis, left parenthesis 80 comma 20 right parenthesis, and left parenthesis 100 comma 0 right parenthesis. The dotted line passes through left parenthesis 20 comma 60 right parenthesis, left parenthesis 50 comma 40 right parenthesis, and left parenthesis 100 comma 10 right parenthesis. A point is plotted where the solid line and the dotted line intersect at left parenthesis 75 comma 25 right parenthesis.
Interpret the graph to find the solution for the following scenario. How do you know this is a reasonable answer?
The players on a softball team held a car wash to raise money for new uniforms. They charged $5 per car and $8 per truck or SUV. If they earned a total of $575 by washing 100 vehicles, how many cars and how many trucks/SUVs did they wash? Let x represent the number of cars and y represent the number of trucks/SUVs.
(1 point)
Responses
(25,75); This is a reasonable answer because if you substitute the numbers for x and y in each equation, the equations are true.
left parenthesis 25 comma 75 right parenthesis ; This is a reasonable answer because if you substitute the numbers for x and y in each equation, the equations are true.
(75,25); This is a reasonable answer because if you substitute the numbers for x and y in each equation, the equations are true.
left parenthesis 75 comma 25 right parenthesis ; This is a reasonable answer because if you substitute the numbers for x and y in each equation, the equations are true.
(80,20); This is a reasonable answer because if you substitute the numbers for x and y in the equation x+y=100, the equation is true.
left parenthesis 80 comma 20 right parenthesis ; This is a reasonable answer because if you substitute the numbers for x and y in the equation x plus y equals 100 , the equation is true.
(35,50); This is a reasonable answer because if you substitute the numbers for x and y in the equation 5x+8y=575, the equation is true.
left parenthesis 35 comma 50 right parenthesis ; This is a reasonable answer because if you substitute the numbers for x and y in the equation 5 x plus 8 y equals 575 , the equation is true.
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