Asked by Mujika
Estimate the solution to the system of these linear equations based on the graph. y=−5x+7 y=−2x+10
Answers
Answered by
Mujika
heres the options
Responses (1,−12) left parenthesis 1 comma negative 12 right parenthesis (−1, 12) left parenthesis negative 1 comma 12 right parenthesis (12,−1) left parenthesis 12 comma negative 1 right parenthesis (−1,−12)
Responses (1,−12) left parenthesis 1 comma negative 12 right parenthesis (−1, 12) left parenthesis negative 1 comma 12 right parenthesis (12,−1) left parenthesis 12 comma negative 1 right parenthesis (−1,−12)
Answered by
GPT 3.5
To estimate the solution to the system of linear equations, we need to determine the point at which the two lines intersect on the graph. By observing the equations, we can see that the slope of the first line is -5 and the y-intercept is 7, while the slope of the second line is -2 and the y-intercept is 10.
Comparing the slopes, we can see that the second line is "shallower" or less steep than the first line. This means the lines will intersect at a point where the x-value is greater than if the second line had a steeper slope.
Observing the y-intercepts, we can see that the second line intersects the y-axis at a higher point, or has a higher y-value when x=0.
Based on these observations, we can estimate that the solution to the system of equations will have an x-value larger than 0 and a y-value larger than 10.
However, without an actual graph to reference, it is difficult to provide a more precise estimate of the solution.
Comparing the slopes, we can see that the second line is "shallower" or less steep than the first line. This means the lines will intersect at a point where the x-value is greater than if the second line had a steeper slope.
Observing the y-intercepts, we can see that the second line intersects the y-axis at a higher point, or has a higher y-value when x=0.
Based on these observations, we can estimate that the solution to the system of equations will have an x-value larger than 0 and a y-value larger than 10.
However, without an actual graph to reference, it is difficult to provide a more precise estimate of the solution.
Answered by
GPT 3.5
Since we do not have a graph to refer to, we can estimate the solution based on the given options.
Looking at the equations, we can see that the slopes of the lines are different, implying that they will intersect at a specific point.
To eliminate some options, let's substitute the x and y values from the given options into the equations to see if they satisfy both equations:
1) (1,−12):
For y = -5x + 7:
-12 = -5(1) + 7
-12 = -5 + 7
-12 = 2 (not satisfied)
For y = -2x + 10:
-12 = -2(1) + 10
-12 = -2 + 10
-12 = 8 (not satisfied)
2) (−1, 12):
For y = -5x + 7:
12 = -5(-1) + 7
12 = 5 + 7
12 = 12 (satisfied)
For y = -2x + 10:
12 = -2(-1) + 10
12 = 2 + 10
12 = 12 (satisfied)
Therefore, the estimated solution to the system of equations based on the graph is (-1, 12).
Looking at the equations, we can see that the slopes of the lines are different, implying that they will intersect at a specific point.
To eliminate some options, let's substitute the x and y values from the given options into the equations to see if they satisfy both equations:
1) (1,−12):
For y = -5x + 7:
-12 = -5(1) + 7
-12 = -5 + 7
-12 = 2 (not satisfied)
For y = -2x + 10:
-12 = -2(1) + 10
-12 = -2 + 10
-12 = 8 (not satisfied)
2) (−1, 12):
For y = -5x + 7:
12 = -5(-1) + 7
12 = 5 + 7
12 = 12 (satisfied)
For y = -2x + 10:
12 = -2(-1) + 10
12 = 2 + 10
12 = 12 (satisfied)
Therefore, the estimated solution to the system of equations based on the graph is (-1, 12).