Question

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

Answer 1

This statement is false.

To determine if a system of equations has a solution, we can graph the equations and see if they intersect at a single point. If the lines do not intersect, it means that there is no solution.

Let's graph the two equations:

The first equation y = -x + 3 is a straight line with a y-intercept of 3 and a slope of -1.

The second equation x + y = 8 can be rearranged to y = -x + 8, which is also a straight line with a y-intercept of 8 and a slope of -1.

Now let's graph these two lines on the same coordinate plane:

The graph of y = -x + 3 is a line that intersects the y-axis at (0, 3) and has a negative slope.

The graph of y = -x + 8 is a line that intersects the y-axis at (0, 8) and also has a negative slope.

From the graph, it is clear that the two lines intersect at the point (2, 1). Therefore, the system does have a solution, and the given statement is false.