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 (-1.5, 0) Solution is (-1.5, 0) Solution is (0, 2) Solution is (0, 2) Solution is (-1, -1) Solution is (-1, -1) Skip to navigation
To graphically solve the system of equations, we need to plot the graphs of both equations and find the point at which they intersect.
1. First, let's graph the equation y = -2x - 1. This is a linear equation in slope-intercept form, where m is the slope (-2) and b is the y-intercept (-1). Start by plotting the y-intercept at (0, -1), then use the slope to find additional points. From the y-intercept, move one unit to the right and two units down to get the point (1, -3), then one unit to the right and two units down again to get the point (2, -5). Connect these points to get the graph of the equation.
2. Next, let's graph the equation 3x - y = -7. This equation is not in slope-intercept form, so we need to rearrange it to solve for y. Subtract 3x from both sides to get -y = -3x - 7, then multiply by -1 to get y = 3x + 7. This equation also has a slope m of 3, but a different y-intercept of 7. Start by plotting the y-intercept at (0, 7), then use the slope to find additional points. From the y-intercept, move one unit to the right and three units up to get the point (1, 10), then one unit to the right and three units up again to get the point (2, 13). Connect these points to get the graph of the equation.
3. Finally, find the point where the two graphs intersect. This point represents the solution to the system of equations. From the graph, it appears that the point of intersection is approximately (-1.6, 2.2).
Therefore, the solution to the system of equations graphically is (-1.6, 2.2).
To solve the system of equations graphically, let's plot the two equations on a graphing calculator.
First, let's graph the equation y = -2x - 1. To do this, go to your graphing calculator and enter the equation into the y= function. Make sure the equation is in slope-intercept form (y = mx + b).
Next, let's graph the 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 get -y = -3x - 7. Then, multiply both sides by -1 to get y = 3x + 7. Now, enter this equation into the y= function on your graphing calculator.
Once both equations are graphed, look for the point of intersection on the graph. This point represents the solution to the system of equations.
Based on the coordinates you provided, the solution to the system is (-1.6, 2.2).
To solve the system of equations graphically using a graphing calculator, you can follow these steps:
1. Enter the first equation into your graphing calculator: y = -2x - 1.
2. Enter the second equation into your graphing calculator: 3x - y = -7.
3. Plot the graphs of both equations on the same coordinate plane by selecting the graphing mode on your calculator.
4. The solution to the system of equations corresponds to the point where the two graphs intersect. Look for the point where the graphs cross each other.
5. Once you locate the point of intersection, read the coordinates of that point.
Based on the options provided, it seems that the correct solution is (-1.5, 0), as this is where the two graphs intersect.