Solving the system y=−x+3 and x+y=8 by graphing shows that there is no solution to the system. Is this statement true or false? Explain. (1 point)
The statement is true, because the lines have an intersection point. The statement is true, because the lines have an intersection point. The statement is true, because the lines are parallel. The statement is true, because the lines are parallel. The statement is false, because the lines have an intersection point. The statement is false, because the lines have an intersection point. The statement is false, because the lines are parallel
The statement is false because the lines do have an intersection point. To solve the system by graphing, we can plot the two lines on a coordinate plane and see where they intersect. By doing so, we can see that the point of intersection is (2, 6). Therefore, there is a solution to the system, making the statement false.
The statement is false, because the lines have an intersection point. The system of equations is y = -x + 3 and x + y = 8. By graphing these equations, we can plot the lines and see if they intersect.
For the first equation, y = -x + 3, we can plot points on the line by substituting different values of x and solving for y. For example, if x = 0, then y = -0 + 3 = 3. This gives us one point on the line, which we can plot on a graph.
For the second equation, x + y = 8, we can also plot points by substituting values of x and solving for y. For example, if x = 0, then 0 + y = 8, which gives y = 8. This gives us another point on the line.
Plotting these points and connecting them gives us the lines. By observing the graph, we can see that the lines intersect at the point (2, 6). Therefore, there is a solution to the system of equations, and the statement is false.
The statement is false because the lines actually have an intersection point.
To solve the system of equations y = -x + 3 and x + y = 8 by graphing, we can start by plotting the two equations on a coordinate plane.
For the first equation y = -x + 3, we can start by setting x = 0 and finding the corresponding y-value. Substitute x = 0 into the equation: y = -(0) + 3 = 3.
Similarly, if we set y = 0 and solve for x in the equation x + y = 8, we find x = 8.
Plotting these two points on the graph, we can draw a straight line that passes through both points.
Now, we can observe that the two lines intersect at the point (x,y) = (5,3). This means that there is a solution to the system of equations.
Therefore, the statement that there is no solution to the system is false because the lines do intersect.