Which of these graphs show that the linear system -2x+y=6 and 4X-2y=-12 has an infinite number of solutions
To determine if a linear system has an infinite number of solutions, we need to check if the two equations are equivalent (i.e., they represent the same line).
Let's plot these two equations:
Graph 1:
-2x + y = 6
This equation can be rewritten as y = 2x + 6.
Graph 2:
4x - 2y = -12
This equation can be rewritten as y = 2x + 6.
Both equations have the same slope-intercept form, y = 2x + 6. Therefore, the two equations are equivalent, meaning that they represent the same line.
Since the two equations represent the same line, the linear system has an infinite number of solutions.
To summarize, both graphs show that the linear system -2x + y = 6 and 4x - 2y = -12 has an infinite number of solutions.
To determine if the linear system -2x+y=6 and 4x-2y=-12 has an infinite number of solutions, we can analyze the graphs of the equations. If the graphs are coincident (i.e., the same line), then there are infinite solutions.
We first need to rewrite the equations in slope-intercept form (y = mx + b).
The first equation, -2x+y=6, can be rearranged as y = 2x + 6.
The second equation, 4x-2y=-12, can be rearranged as -2y = -4x - 12 and then y = 2x + 6.
Now that we have both equations in slope-intercept form, we can see that they have the same slope (m = 2) and the same y-intercept (b = 6).
When graphed, these equations will result in the same line, indicating that the linear system has an infinite number of solutions.
Therefore, the correct graph that shows the linear system with an infinite number of solutions would be a single line covering both lines.
To determine which graph represents a linear system with an infinite number of solutions, you need to compare the two equations and check if they are dependent (meaning they represent the same line).
First, let's put both equations in slope-intercept form (y = mx + b).
For the first equation, -2x + y = 6, we can rearrange it to y = 2x + 6.
For the second equation, 4x - 2y = -12, we can rearrange it to -2y = -4x - 12, and then divide everything by -2 to get y = 2x + 6.
As you can observe, both equations have the same slope (2) and the same y-intercept (6). This means that their graphs will be the same line.
Thus, the correct answer is any graph that represents the equation y = 2x + 6.