Solving the system y=-x+3 and x+y=8 by graphing shows that there is no solution to the system is this system true or false explain
This statement is false. Solving the system of equations by graphing involves plotting the two equations on a coordinate plane and finding the point of intersection, if it exists. However, in this case, the two equations intersect at the point (2, 6), which satisfies both equations. Therefore, there is a solution to the system of equations.
To determine if the statement is true or false, we need to graph the given system of equations and analyze the intersection point (if any).
First, let's graph the two equations separately:
1. Start with the equation y = -x + 3. For this equation, we can start by plotting two points: (0, 3) and (3, 0), and then draw a straight line passing through these points.
2. Now, let's graph the equation x + y = 8. Similarly, plot two points: (0, 8) and (8, 0), and draw a straight line through them.
Next, we'll examine the graph and look for the intersection point(s). If there is an intersection point, it means that there is a solution to the system. If there is no intersection point, then there is no solution.
Upon observing the graph, it becomes apparent that the two lines intersect at the point (2, 6). Therefore, there is an intersection, and thus, the statement "there is no solution to the system" is false.
In summary, the statement is false because the system does have a solution, which occurs at the point (2, 6).
To determine if the system y = -x + 3 and x + y = 8 has a solution, we can graph the two equations and observe their intersection point.
Let's start by graphing the equation y = -x + 3:
- To do this, we'll plot a few points that satisfy this equation. For example, when x = 0, y = -0 + 3 = 3, so we plot the point (0, 3). When x = 1, y = -1 + 3 = 2, so we plot the point (1, 2), and so on.
- Once we have a few points, we can connect them with a straight line to create the graph.
Next, let's graph the equation x + y = 8:
- Similarly, we'll find a few points that satisfy this equation. For example, when x = 0, y = 8 - 0 = 8, so we plot the point (0, 8). When x = 1, y = 8 - 1 = 7, so we plot the point (1, 7), and so on.
- Again, we connect these points to create the graph.
Now, if the graphs of the two equations intersect at a point, that means there is a solution to the system. However, if the graphs do not intersect, no solution exists.
Upon graphing these two equations, we can observe that the lines are parallel and never intersect (graphs can be plotted using graphing software or drawn by hand). Therefore, there is no point where these two lines cross each other, indicating that the system has no solution.
Hence, the statement "there is no solution to the system" is true for the given system of equations.