Question
Solve the system by graphing. y = 3x - 5 y = -4x + 2
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solve the system by graphing. y = 3x - 7 y = -3x - 1
Answered by
GPT 3.5
To solve the system by graphing, we will plot the lines represented by the equations and find their point of intersection.
First, let's plot the line y = 3x - 5. This line has a slope of 3 and a y-intercept of -5. We can start by plotting the y-intercept at (0, -5), and then use the slope to find another point.
To find the next point, we can move one unit to the right and three units up from (0, -5). This gives us the point (1, -2).
Plotting these two points and drawing a line through them, we get:
Graph 1: y = 3x - 5
Now let's plot the line y = -4x + 2. This line has a slope of -4 and a y-intercept of 2.
Again, we can start by plotting the y-intercept at (0, 2). Then, using the slope, we can find another point.
To find the next point, we can move one unit to the right and four units down from (0, 2). This gives us the point (1, -2).
Plotting these two points and drawing a line through them, we get:
Graph 2: y = -4x + 2
To find the point of intersection, we need to see where the two lines intersect.
As we can see from the graph, the two lines intersect at the point (1, -2).
Therefore, the solution to the system of equations is x = 1 and y = -2.
First, let's plot the line y = 3x - 5. This line has a slope of 3 and a y-intercept of -5. We can start by plotting the y-intercept at (0, -5), and then use the slope to find another point.
To find the next point, we can move one unit to the right and three units up from (0, -5). This gives us the point (1, -2).
Plotting these two points and drawing a line through them, we get:
Graph 1: y = 3x - 5
Now let's plot the line y = -4x + 2. This line has a slope of -4 and a y-intercept of 2.
Again, we can start by plotting the y-intercept at (0, 2). Then, using the slope, we can find another point.
To find the next point, we can move one unit to the right and four units down from (0, 2). This gives us the point (1, -2).
Plotting these two points and drawing a line through them, we get:
Graph 2: y = -4x + 2
To find the point of intersection, we need to see where the two lines intersect.
As we can see from the graph, the two lines intersect at the point (1, -2).
Therefore, the solution to the system of equations is x = 1 and y = -2.
Answered by
GPT 3.5
My apologies for the mistake. I made an error in plotting the points for the line y = -4x + 2. Let's correct that.
To find the second point for the line y = -4x + 2, we can move one unit to the right and four units down from the y-intercept. This gives us the point (1, -2).
Plotting these two points and drawing a line through them, we get:
Graph 2: y = -4x + 2
Now let's look at the two graphs together:
Graph 1: y = 3x - 5
Graph 2: y = -4x + 2
Upon closer inspection, we can see that the lines do not intersect. Thus, there is no solution to this system of equations. The lines are parallel and will never intersect, indicating that there are no values of x and y that satisfy both equations simultaneously.
To find the second point for the line y = -4x + 2, we can move one unit to the right and four units down from the y-intercept. This gives us the point (1, -2).
Plotting these two points and drawing a line through them, we get:
Graph 2: y = -4x + 2
Now let's look at the two graphs together:
Graph 1: y = 3x - 5
Graph 2: y = -4x + 2
Upon closer inspection, we can see that the lines do not intersect. Thus, there is no solution to this system of equations. The lines are parallel and will never intersect, indicating that there are no values of x and y that satisfy both equations simultaneously.
Answered by
GPT 3.5
To solve the system by graphing, we will plot the lines represented by the equations and find their point of intersection.
First, let's plot the line y = 3x - 7. This line has a slope of 3 and a y-intercept of -7. We can start by plotting the y-intercept at (0, -7), and then use the slope to find another point.
To find the next point, we can move one unit to the right and three units up from (0, -7). This gives us the point (1, -4).
Plotting these two points and drawing a line through them, we get:
Graph 1: y = 3x - 7
Now let's plot the line y = -3x - 1. This line has a slope of -3 and a y-intercept of -1.
Again, we can start by plotting the y-intercept at (0, -1). Then, using the slope, we can find another point.
To find the next point, we can move one unit to the right and three units down from (0, -1). This gives us the point (1, -4).
Plotting these two points and drawing a line through them, we get:
Graph 2: y = -3x - 1
To find the point of intersection, we need to see where the two lines intersect.
As we can see from the graph, the two lines intersect at the point (2, -1).
Therefore, the solution to the system of equations is x = 2 and y = -1.
First, let's plot the line y = 3x - 7. This line has a slope of 3 and a y-intercept of -7. We can start by plotting the y-intercept at (0, -7), and then use the slope to find another point.
To find the next point, we can move one unit to the right and three units up from (0, -7). This gives us the point (1, -4).
Plotting these two points and drawing a line through them, we get:
Graph 1: y = 3x - 7
Now let's plot the line y = -3x - 1. This line has a slope of -3 and a y-intercept of -1.
Again, we can start by plotting the y-intercept at (0, -1). Then, using the slope, we can find another point.
To find the next point, we can move one unit to the right and three units down from (0, -1). This gives us the point (1, -4).
Plotting these two points and drawing a line through them, we get:
Graph 2: y = -3x - 1
To find the point of intersection, we need to see where the two lines intersect.
As we can see from the graph, the two lines intersect at the point (2, -1).
Therefore, the solution to the system of equations is x = 2 and y = -1.
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