Solve the system of equations by graphing. Then classify the system. x+y=9 x-y=3 Use graphing tool to graph the system
Just mentally add them to get
2x = 12
x = 6, then mentally 6+y = 9 ---> y = 3
Unless the purpose of graphing these two simple equations is to illustrate how graphing two lines shows their intersection as the solution to the system of equations, in this case "graphing" would be my last choice to solve the system.
Secondly, how do you expect us to know which "graphing tool" is available to you.
My favourite would be a sheet of graphing paper, and a sharp pencil
We have no idea what your "graphing tool" is, but surely you can plot both equations and see where they intersect. Alternatively, note that 2x = 12, so that x = 6.
To solve the system of equations by graphing, we will individually graph each equation on the same coordinate plane. Then, we will find the point where the two graphs intersect.
Let's start with the first equation: x + y = 9.
To graph this equation, we need to rearrange it into slope-intercept form (y = mx + b), where m is the slope, and b is the y-intercept.
x + y = 9 --> y = -x + 9.
The slope-intercept form tells us that the slope is -1, and the y-intercept is 9. Plotting the y-intercept at point (0, 9) on the graph, we can use the slope to find one more point.
Since the slope is -1, we can move down 1 and right 1 to reach the next point. Plotting this second point, we can draw a straight line through the two points to represent the equation x + y = 9.
Now, let's move on to the second equation: x - y = 3.
Rearranging this equation into slope-intercept form, we have:
y = x - 3.
Here, the slope is 1, and the y-intercept is -3. Plot the y-intercept at point (0, -3), and use the slope to find the next point.
Since the slope is 1, we move up 1 and right 1 to reach the next point. Plotting this second point, we can draw a straight line through the two points to represent the equation x - y = 3.
Now, we can see the two lines intersect on the graph. The point of intersection is (6, 3).
This system of equations is classified as consistent and independent since there is exactly one solution that satisfies both equations.
To solve the system of equations by graphing, we can plot the two equations on a coordinate plane and look for the point where they intersect. This point represents the solution to the system.
Given the system of equations:
1. x + y = 9
2. x - y = 3
To plot the first equation, rearrange it in the form y = mx + b, where 'm' represents the slope and 'b' represents the y-intercept.
1. x + y = 9
y = -x + 9
To plot the second equation:
2. x - y = 3
y = x - 3
Now, we can use a graphing tool or manually plot these equations on a coordinate plane. Let's assume we are using a graphing tool:
- Open a graphing tool or website that allows you to plot equations on a coordinate plane.
- Plot the first equation y = -x + 9. To do this, set the y-intercept at 9 and use the slope as -1 (because the coefficient of x is -1 in this equation).
- Plot the second equation y = x - 3. Set the y-intercept at -3 and the slope as 1.
Once you have plotted these equations, the point where the lines intersect represents the solution to the system of equations. The intersection point can be determined by analyzing the coordinates of that point on the graph.
To classify the system of equations, we need to determine whether it has a unique solution, no solution, or infinitely many solutions. Since we are using graphing, we can easily visualize the nature of the system.
- If the lines intersect at a single point, the system has a unique solution.
- If the lines are parallel and do not intersect, the system has no solution.
- If the lines coincide (overlap perfectly), the system has infinitely many solutions.
By analyzing the graph, we can determine the nature of the system.