Bot help
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
The graph that shows that the linear system y = -x + 6 and 3x + 3y = 18 has an infinite number of solutions is the first graph option: O O
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 analyze the equations and look for characteristics that indicate infinite solutions.
Let's simplify the equations first:
Equation 1: y = -x + 6
Equation 2: 3x + 3y = 18
Considering Equation 2, we can divide both sides by 3 to make the coefficients of x and y equal to 1:
x + y = 6
Now, we have the following system of equations:
Equation 1: y = -x + 6
Equation 2 (simplified): x + y = 6
To find a graph that represents the system with an infinite number of solutions, we need to look for graphs where the lines representing the equations are coincident or overlapping. This occurs when the slope and y-intercept of the lines are the same.
Comparing the equations, both have the same slope of -1. Therefore, we need to find a graph where the lines have the same y-intercept of 6.
Based on the provided graphs, the second option seems to satisfy the conditions. the graph that shows a line passing through the point (0, 6) and having a slope of -1 indicates that the linear system has an infinite number of solutions.
Therefore, the correct graph is:
O y
|
|
10|
|
9 |
|
8 |
|
7o-
|-------
| \
| \
6 | \
| \
5 | \
| \
4 | \
| \
3 | \
| \
2 | \
| \
1 |--------------------\
|
|
|
-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4
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 the concept of a linear system and how it is represented graphically.
First, let's rewrite the second equation in slope-intercept form (y = mx + b):
3x + 3y = 18
Dividing both sides of the equation by 3, we get:
x + y = 6
Rearranging the equation, we have:
y = -x + 6
The two equations y = -x + 6 and y = -x + 6 represent the same line. This means that the two equations are dependent and have an infinite number of solutions.
Now, let's analyze the given graphs to determine which one represents this situation.
Graph 1:
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
Graph 2:
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
Graph 3:
-14 -4- -5- -6 -7- -8- -9- -10- 1 + fennhaug 2 3 6 7 8 9 10 x
Based on the graphs provided, Graph 2 represents the linear system y = -x + 6 and 3x + 3y = 18 having an infinite number of solutions. This is because the graph shows a single straight line, which corresponds to both equations being dependent and having the same solution set.
Therefore, Graph 2 is the correct answer.