Solve the system of equations graphically. You can use your graphing calculator!
y=−2x−1
3x − y =−7
To solve the system of equations graphically using a graphing calculator, follow these steps:
1. Turn on your graphing calculator and enter the first equation: y = -2x - 1. Make sure the equation is in the form y = mx + b, where m is the slope and b is the y-intercept.
2. Graph the equation by selecting the graphing option on your calculator. The line should appear on the graph.
3. Now enter the second equation: 3x - y = -7. To graph this equation, we need to rewrite it in slope-intercept form. Subtract 3x from both sides of the equation to isolate the y term: y = 3x + 7.
4. Enter the new equation into your calculator and graph it as well.
5. Once both equations are graphed, look for the point where the lines intersect. This point represents the solution to the system of equations.
Note: Different graphing calculators may have slightly different steps or interface, but the general process should be the same.
To solve the system of equations graphically using a graphing calculator, follow these steps:
1. Turn on your graphing calculator and make sure it is in function mode.
2. Enter the first equation, y = -2x - 1, into a Y-variable. For example, you can enter it as Y1.
3. Enter the second equation, 3x - y = -7, into another Y-variable. Let's use Y2.
4. Press the graph button (usually denoted as "GRAPH" or "DRAW") to graph both equations on the same coordinate plane.
5. Once the graph appears, you can adjust the window or zoom in/out to get a better view of the intersection point, if necessary.
6. Look for the point where the two graphs intersect. This point represents the solution to the system of equations.
7. If needed, use the trace function on your calculator to get the coordinates of the intersection point.
By following these steps, you can use your graphing calculator to solve the system of equations graphically.
To solve the system of equations graphically, we will graph both equations and look for the point where the two lines intersect.
First, let's graph the equation y = -2x - 1:
- Start by choosing some x-values and substituting them into the equation to find the corresponding y-values. We'll choose x = -3, -2, 0, 1, 2:
For x = -3: y = -2(-3) - 1 = 5
For x = -2: y = -2(-2) - 1 = 3
For x = 0: y = -2(0) - 1 = -1
For x = 1: y = -2(1) - 1 = -3
For x = 2: y = -2(2) - 1 = -5
Plot these points on the coordinate plane and draw a line that passes through them:
(-3, 5)
|
(-2, 3)
|
(0, -1)
|
(1, -3)
|
(2, -5)
|
-----------------------------------
Next, let's graph the equation 3x - y = -7:
- To graph this equation, solve for y:
y = 3x + 7
Again, choose some x-values and substitute them into the equation to find the corresponding y-values. We'll choose x = -3, -2, 0, 1, 2:
For x = -3: y = 3(-3) + 7 = -2
For x = -2: y = 3(-2) + 7 = 1
For x = 0: y = 3(0) + 7 = 7
For x = 1: y = 3(1) + 7 = 10
For x = 2: y = 3(2) + 7 = 13
Plot these points on the coordinate plane and draw a line that passes through them:
(-3, -2)
|
(-2, 1)
|
(0, 7)
|
(1, 10)
|
(2, 13)
|
-----------------------------------
Now, we can see that the two lines intersect at approximately (-2, 3). This is the solution to the system of equations.