Solving the system Y equals negative X +3 and X plus Y equals eight by graphing shows that there are no solutions to the system. Is this statement true or false explain

Answer 1

This statement is false. Let's solve the system of equations:

1) Y = -X + 3
2) X + Y = 8

We can graph these equations on a coordinate plane by finding at least two points that satisfy each equation.

For equation (1), when X = 0, we have Y = 3. When X = 1, we have Y = 2. Plotting these points, we get the line:

(0, 3) and (1, 2)

For equation (2), if X = 0, we have Y = 8. If X = 1, we have Y = 7. Plotting these points, we get the line:

(0, 8) and (1, 7)

Now, let's see where the lines intersect. From the graph, it is clear that the lines intersect at the point (2, 6).

Thus, there is one solution to the system of equations. Therefore, the statement "there are no solutions to the system" is false.