Solve the system of equations graphically. Y=-2x-1. 3x-y=-7
To solve the system of equations graphically, we need to graph the two equations and find the point where they intersect.
First, let's graph the equation y = -2x - 1. We can start by assigning values to x and finding the corresponding values of y:
When x = 0, y = -2(0) - 1 = -1. So one point on the graph is (0, -1).
When x = 1, y = -2(1) - 1 = -3. So another point on the graph is (1, -3).
We can now plot these two points on a graph and draw a line passing through them:
(0, -1) and (1, -3)
Next, let's graph the equation 3x - y = -7. Again, we can assign values to x and find corresponding values of y:
When x = 0, 3(0) - y = -7, which gives us y = 7. So one point on the graph is (0, 7).
When x = 1, 3(1) - y = -7, which gives us y = 10. So another point on the graph is (1, 10).
Plot these two points and draw a line passing through them:
(0, 7) and (1, 10)
The point where the two lines intersect is the solution to the system of equations. By observing the graph, we can estimate that the intersection point is approximately (2, -5).
Thus, the solution to the system of equations is x = 2 and y = -5.
To solve the system of equations graphically, we'll plot the equations on a graph and find the point of intersection.
Equation 1: y = -2x - 1
Equation 2: 3x - y = -7
Let's rearrange Equation 2 to isolate y:
y = 3x + 7
Now we can graph these equations:
For Equation 1:
Pick some x-values (let's choose -2, 0, and 2) and substitute into the equation to find the corresponding y-values:
For x = -2:
y = -2(-2) - 1 = 4 - 1 = 3
So we have the point (-2, 3).
For x = 0:
y = -2(0) - 1 = 0 - 1 = -1
So we have the point (0, -1).
For x = 2:
y = -2(2) - 1 = -4 - 1 = -5
So we have the point (2, -5).
For Equation 2:
Again, pick some x-values and substitute into the equation to find the corresponding y-values:
For x = -2:
y = 3(-2) + 7 = -6 + 7 = 1
So we have the point (-2, 1).
For x = 0:
y = 3(0) + 7 = 0 + 7 = 7
So we have the point (0, 7).
For x = 2:
y = 3(2) + 7 = 6 + 7 = 13
So we have the point (2, 13).
Now, plot these points on a graph and draw a line passing through each set of points for each equation.
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13| ● (2, 13)
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| ● (2, -5)
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| ● (0, 7)
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| ● (0, -1)
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| ● (-2, 3)
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Now, we can see that the lines intersect at the point (2, -5). Thus, the solution to the system of equations is x = 2 and y = -5.
To solve the system of equations graphically, we can plot their graphs on a coordinate plane and find the point of intersection, which represents the solution of the system.
Let's start by graphing the first equation, y = -2x - 1. To do this, we need to find at least two points that satisfy this equation.
To find the points, we can randomly choose values for x and substitute them into the equation to find the corresponding y-values. Let's choose x = 0 and x = 1:
When x = 0:
y = -2(0) - 1 = -1
So, the first point is (0, -1).
When x = 1:
y = -2(1) - 1 = -3
So, the second point is (1, -3).
Now, we plot these two points on the coordinate plane:
(0, -1) and (1, -3)
Next, let's graph the second equation, 3x - y = -7. We can rearrange this equation to solve for y:
y = 3x + 7
Again, we choose two x-values and find the corresponding y-values. Let's use x = 0 and x = 1:
When x = 0:
y = 3(0) + 7 = 7
So, the third point is (0, 7).
When x = 1:
y = 3(1) + 7 = 10
So, the fourth point is (1, 10).
Plotting these two points on the same coordinate plane, we have:
(0, 7) and (1, 10)
Now, we have both equations graphed on the coordinate plane. To find the solution, we look for the point where the two lines intersect. In this case, it appears that the lines intersect at approximately (2, -5).
Therefore, the solution to the system of equations is x = 2 and y = -5.
Note: The accuracy of the solution may vary depending on the precision of the graphing method used.