Solve the system of equations graphically.
y=−2x−1
3x − y =−7
To solve the system of equations graphically, we need to graph both equations on the same coordinate plane and find the point of intersection, which represents the solution to the system.
First, let's graph the equation y = -2x - 1.
To do this, we can start by finding the y-intercept, which is -1. This means that the line intersects the y-axis at the point (0, -1).
Next, we can find the x-intercept by setting y = 0 and solving for x:
0 = -2x - 1
2x = -1
x = -1/2
This gives us the x-intercept at the point (-1/2, 0).
We can now plot these two points on the coordinate plane and draw a straight line through them.
Next, let's graph the equation 3x - y = -7.
We can rewrite this equation in the form y = mx + b:
y = 3x + 7
To graph this equation, we can start by finding the y-intercept, which is 7. This means that the line intersects the y-axis at the point (0, 7).
Next, we can find the x-intercept by setting y = 0 and solving for x:
0 = 3x + 7
-7 = 3x
x = -7/3
This gives us the x-intercept at the point (-7/3, 0).
We can now plot these two points on the coordinate plane and draw a straight line through them.
Now that we have graphed both equations, we can identify the point of intersection.
The point where the two lines intersect is approximately (-2, 3).
Therefore, the solution to the system of equations is x = -2 and y = 3.
To solve the system of equations graphically, we will plot the graphs of the two equations and find their point of intersection.
First, let's rewrite the equations in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
1. Equation 1: y = -2x - 1
Slope (m1): -2
Y-intercept (b1): -1
2. Equation 2: 3x - y = -7
Convert it to slope-intercept form:
-y = -3x - 7
Divide by -1 to isolate y:
y = 3x + 7
Slope (m2): 3
Y-intercept (b2): 7
Now, let's plot the graphs:
Equation 1: y = -2x - 1
Starting with the y-intercept (0, -1), plot this point on the graph. Then, use the slope to plot more points. Since the slope is -2, you can go down 2 units and right 1 unit. Connect the points to form a line.
Equation 2: y = 3x + 7
Starting with the y-intercept (0, 7), plot this point on the graph. Then, use the slope to plot more points. Since the slope is 3, you can go up 3 units and right 1 unit. Connect the points to form a line.
Once both lines are plotted, see where they intersect. That point is the solution to the system of equations.
I hope this helps! Let me know if you have any other questions.
To solve the system of equations graphically, we need to plot the equations on a graph and find the intersection point(s) of the two lines.
Let's start with the first equation: y = -2x - 1
To plot this equation, we can choose some values for x and find the corresponding values for y. Let's choose three values for x: -2, 0, and 2.
For x = -2:
y = -2(-2) - 1 = 4 - 1 = 3
So one point is (-2, 3).
For x = 0:
y = -2(0) - 1 = 0 - 1 = -1
So another point is (0, -1).
For x = 2:
y = -2(2) - 1 = -4 - 1 = -5
So the third point is (2, -5).
Now, let's plot those points on a graph.
Next, let's move on to the second equation: 3x - y = -7
To plot this equation, we can again choose some values for x and find the corresponding values for y. Let's choose the same three values for x: -2, 0, and 2.
For x = -2:
3(-2) - y = -7
-6 - y = -7
-y = -7 + 6
-y = -1
y = 1
So another point is (-2, 1).
For x = 0:
3(0) - y = -7
0 - y = -7
-y = -7
y = 7
So another point is (0, 7).
For x = 2:
3(2) - y = -7
6 - y = -7
-y = -7 - 6
-y = -13
y = 13
So the third point is (2, 13).
Let's plot those points on the same graph.
Now, we can see that the two lines intersect at a single point: (-3, 5).
Therefore, the solution to the system of equations is x = -3 and y = 5.