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Which of these graphs shows that the linear system -2x + y = 6 and 4x - 2y = -12 has an infinite number of solutions? (1 point) O O y 10- -9- -8 --7- -6₂ -5- -4 -3 2 -1- -0- -10-9 -8 -7 -6 -5 -4 -3 -2 -1,0 F-14 ن من -2- -3- -4- -5- -6- -7- -8- -9- -10- y 4 10- -9- -8- 7- -6- -5- -4- -3- 2- 23 -2- -3- -4- -5- 1 -1 -0- -10-9-8-7 -6 -5 -4 -3 -2 -1,0 1 2 3 4 5 6 7 8 9 10 -14 -6₂ -7. -8- -9- -10- 2 3 4 5 6 7 8 9 10 x
Based on the given linear system -2x + y = 6 and 4x - 2y = -12, the graph that shows an infinite number of solutions is the one with intersecting lines.
The graph that matches this description is the second one.
To determine which graph shows that the linear system -2x + y = 6 and 4x - 2y = -12 has an infinite number of solutions, we can use the method of graphing.
First, let's rewrite both equations in slope-intercept form (y = mx + b):
For -2x + y = 6:
y = 2x + 6
For 4x - 2y = -12:
-2y = -4x -12
y = 2x + 6
Both equations have the same slope (m = 2) and the same y-intercept (b = 6), which means their graphs will be identical and they will intersect at every point. Therefore, the linear system has an infinite number of solutions.
Based on this information, the graph that represents an infinite number of solutions is the one where the lines representing the two equations overlap completely.
Unfortunately, the text description of the graphs provided is not clear or readable. Please provide a clear and readable description or any additional information, or if possible, provide a link or image of the graphs in question.
To determine which graph shows that the linear system -2x + y = 6 and 4x - 2y = -12 has an infinite number of solutions, we need to find out if the two equations represent parallel lines or the same line.
To do this, we need to put the equations in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
For the first equation, -2x + y = 6, we can rearrange it to solve for y: y = 2x + 6.
For the second equation, 4x - 2y = -12, we can also rearrange it to solve for y: y = 2x + 6.
Both equations have the same slope (m = 2), and the same y-intercept (b = 6). This means that the two lines are identical and overlap, indicating that there are infinite solutions.
From the given graphs, we need to look for the one where the lines are overlapping or identical.
Looking at the options:
Option O O
Option O y 10- -9- -8 --7- -6₂ -5- -4 -3 2 -1- -0- -10-9 -8 -7 -6 -5 -4 -3 -2 -1,0
Option F-14 ن من -2- -3- -4- -5- -6- -7- -8- -9- -10- y 4 10- -9- -8- 7- -6- -5- -4- -3- 2- 23 -2- -3- -4- -5- 1 -1 -0- -10-9-8-7 -6 -5 -4 -3 -2 -1,0 1 2 3 4 5 6 7 8 9 10
Option -14 -6₂ -7. -8- -9- -10- 2 3 4 5 6 7 8 9 10 x
The correct answer is Option O O, which shows the lines overlapping each other and indicating an infinite number of solutions.
Therefore, the correct graph is the one labeled Option O O.