Solve the system of equations graphically. You can use your graphing calculator! y=−2x−1 3x − y =−7 (1 point) Responses Solution is (-1.6, 2.2 ) Solution is (-1.6, 2.2 ) Solution is (0, 2) Solution is (0, 2) Solution is (-1, -1) Solution is (-1, -1) Solution is (-1.5, 0) Solution is (-1.5, 0) Skip to navigation
To graph the system of equations, we need to plot the lines y = -2x - 1 and 3x - y = -7.
First, let's graph the line y = -2x - 1. To do this, plot two points on the line. One easy way to do this is by setting x = 0 and solving for y, and setting x = 1 and solving for y.
When x = 0, y = -2(0) - 1 = -1. This gives us the point (0, -1).
When x = 1, y = -2(1) - 1 = -3. This gives us the point (1, -3).
Plotting these two points and drawing a line through them, we get:
The first solution given, (-1.6, 2.2), does not seem to be on the graph.
Now, let's graph the line 3x - y = -7. To do this, we again choose values for x and solve for y.
When x = 0, y = 3(0) - (-7) = 7. This gives us the point (0, 7).
When x = 1, y = 3(1) - (-7) = 10. This gives us the point (1, 10).
Plotting these two points and drawing a line through them, we get:
The second solution given, (0, 2), does not seem to be on the graph.
The third solution given, (-1, -1), does not seem to be on the graph.
The fourth solution given, (-1.5, 0), does not seem to be on the graph.
Therefore, none of the given solutions seem to accurately represent the solution to the system of equations when graphed.
To solve the system of equations graphically, we can graph each equation and find the point(s) where they intersect. These intersection points represent the solutions to the system.
First, let's graph the equation y = -2x - 1. To do this, plot a few points on the graph:
When x = 0, y = -2(0) - 1 = -1. So we have the point (0, -1).
When x = -1, y = -2(-1) - 1 = 1. So we have the point (-1, 1).
Plotting these points and drawing a line through them, we get the first graph:
Next, let's graph the equation 3x - y = -7. We can rearrange this equation to y = 3x + 7. Again, plot a few points:
When x = 0, y = 3(0) +7 = 7. So we have the point (0, 7).
When x = -1, y = 3(-1) + 7 = 4. So we have the point (-1,4).
Plotting these points and drawing a line through them, we get the second graph:
Now, we can see the intersection point of these lines by looking at the graph. From the graph, it looks like the intersection point is around (-1.6, 2.2). Therefore, the solution to the system of equations is (-1.6, 2.2).
To solve the system of equations graphically, we need to plot the graphs of both equations on the same coordinate plane and find the point of intersection. This point represents the solution to the system.
Let's start with the first equation: y = -2x - 1.
To plot this line, we can assign different values to x and then calculate the corresponding y values. Alternatively, we can rearrange the equation to find the y-intercept and the slope.
The equation is already in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
In this case, the slope is -2 and the y-intercept is -1 (since b = -1). So we can start by plotting the point (0, -1) and then use the slope to find more points.
Using the slope of -2, we can go down 2 units and right 1 unit to find another point. Doing this a few times, we can plot more points and draw a line through them.
Now let's move on to the second equation: 3x - y = -7.
We need to rearrange the equation in slope-intercept form. Subtract 3x from both sides to isolate y:
-y = -3x - 7
Multiplying both sides by -1, the equation becomes:
y = 3x + 7
Now we can see that the slope is 3 and the y-intercept is 7. Plotting the point (0, 7) and using the slope of 3, we can find more points and draw the line.
Now that we have both lines plotted on the graph, we can visually determine the point of intersection. This point represents the solution to the system of equations.
Using a graphing calculator or any graphing tool, find the point where the two lines intersect. This point will give you the solution to the system of equations.
In this case, the solution is approximately (-1.6, 2.2) on the coordinate plane.
So, the correct response is "Solution is (-1.6, 2.2)".