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Which of these graphs shows that the linear system y = -x + 6 and 3x + 3y = 18 has an infinite number of solutions? (1 point) O O y 10- -9- -8- 7. -6 -5- 4² -3- 2- -1. -0- -10-9 -8 -7 -6 -5 -4 -3 -2 -1,0 -1- -2- -3- -4- -5- -6- -7- -8- -9- -10- 2 3 4 a- -2- -3- 10- -9- -8- 7- 6- -5- -4- -3- 2- -1- -0- -10-9-8-7 -6 -5 -4 -3 -2 -1,0 1 2 3 4 5 6 7 8 9 10 -14 -4- -5- -6 -7- -8- -9- -10- 1 + fennhaug 2 3 6 7 8 9 10 x
Based on the given options, the graph that shows an infinite number of solutions for the linear system is:
2 3 6 7 8 9 10
-14 -4- -5- -6 -7- -8- -9- -10- 1
This graph represents the same line for both equations in the system, indicating that there are infinitely many solutions.
To determine which graph shows that the linear system y = -x + 6 and 3x + 3y = 18 has an infinite number of solutions, we need to find the graph where the two equations are equivalent.
First, let's transform the equations into slope-intercept form (y = mx + b):
y = -x + 6
3x + 3y = 18
Divide both sides by 3:
x + y = 6
Solve for y:
y = -x + 6
Comparing the two equations, we see that they are the same. This means that the system has infinitely many solutions.
Looking at the given graphs, the graph that represents the equations y = -x + 6 and 3x + 3y = 18 having an infinite number of solutions is the one where the lines overlap completely. Unfortunately, without a visual representation of the graphs, it is difficult to pinpoint the exact graph. However, it should be the one where the lines overlap or coincide.
To determine which graph shows that the linear system y = -x + 6 and 3x + 3y = 18 has an infinite number of solutions, we need to understand what it means for a system to have infinitely many solutions and how to graph the given lines.
A linear system has infinitely many solutions when the two equations represent the same line. This means that the lines are coincident, and they will intersect at every point along the line. Graphically, this appears as one line overlapping the other.
To graph y = -x + 6 and 3x + 3y = 18, we can use the slope-intercept form (y = mx + b) and the standard form (Ax + By = C) of linear equations, respectively.
1. y = -x + 6:
This equation is already in slope-intercept form, where the slope (m) is -1 and the y-intercept (b) is 6. We can plot two points on this line using the slope and the y-intercept:
- Start at the y-intercept (0, 6)
- Use the slope to find a second point: move one unit to the right and one unit down from the y-intercept, giving us (1, 5).
2. 3x + 3y = 18:
We need to rearrange this equation into slope-intercept form. Divide the entire equation by 3 to simplify, giving us x + y = 6. Then, subtract x from both sides to isolate y: y = -x + 6. This equation represents the exact same line as the first one.
Now, we can analyze the given graphs and see which one represents the situation of overlapping lines, indicating an infinite number of solutions. Unfortunately, the graphs you provided are not visible through text, so I am unable to identify the correct graph without further information. However, you can analyze the graphs by identifying if the lines overlap or intersect at every point along the line.
Make sure to view the graphs visually or provide additional details, so I can assist you further in determining the correct graph.