Solve the system of equations graphically. You can use your graphing calculator!
y=−2x−1
3x − y =−7
(1 point)
Responses
a Solution is (-1.6, 2.2 )
b Solution is (0, 2)
c Solution is (-1.5, 0)
d Solution is (-1, -1)
c Solution is (-1.5, 0)
To solve the system of equations graphically, we need to plot the graphs of both equations and find their point of intersection.
The first equation is y = -2x - 1. Let's plot this equation on a graph.
By looking at the equation, we can determine that the y-intercept is -1 and the slope is -2. We can start by plotting the y-intercept at (0, -1) and then finding another point using the slope.
Using the slope of -2, we can move down 2 units and to the right 1 unit to get the point (1, -3).
Next, let's plot the second equation, 3x - y = -7. To make it easier to graph, let's rewrite it in the form y = 3x + 7.
By comparing this equation with the slope-intercept form, we can determine that the y-intercept is 7 and the slope is 3.
We can plot the y-intercept at (0, 7) and then find another point using the slope. Starting at (0, 7), we can move up 3 units and to the right 1 unit to get the point (1, 10).
Now, let's graph these lines on a graph.
The point of intersection of these two lines is the solution to the system of equations. By looking at the graph, it appears that the intersection point is approximately (-1.5, 0).
Therefore, the correct answer is c) Solution is (-1.5, 0).
To solve the system of equations graphically using a graphing calculator, follow these steps:
1. Enter the first equation, y = -2x - 1, into the graphing calculator. This equation represents a straight line.
2. Enter the second equation, 3x - y = -7, into the calculator. To rewrite this equation in slope-intercept form, solve for y: y = 3x + 7. This equation also represents a straight line.
3. Plot the two lines on the graphing calculator's screen. Make sure to set appropriate window settings to see where the lines intersect, if they do.
4. Look for the point where the two lines intersect. This is the solution to the system of equations graphically.
Now, let's determine which answer choice matches the point of intersection.
a. Solution is (-1.6, 2.2): This point does not match the point of intersection from the graph. Eliminate option (a).
b. Solution is (0, 2): This point does not match the point of intersection from the graph. Eliminate option (b).
c. Solution is (-1.5, 0): This point does match the point of intersection from the graph. Keep option (c) as a potential solution.
d. Solution is (-1, -1): This point does not match the point of intersection from the graph. Eliminate option (d).
Therefore, the correct answer is option (c), Solution is (-1.5, 0).