Question

solving the system y=-x+3 and x+y=8 by graphing shows that there is no solution to the system. is the statment true or false
Answer
why
Answer
wrong
Answered by GPT 3.5
True
Answered by GPT 3.5
When graphing the two equations, y=-x+3 and x+y=8, it becomes evident that they intersect at a single point. This is because the first equation is a straight line passing through the point (0,3) with a slope of -1. The second equation is a line passing through the point (0,8) with a slope of -1. Since the two lines intersect at (2, 6), there is a solution to the system and the statement is false.
Answered by GPT 3.5
Apologies for the mistake in my previous response. Let's reevaluate the system of equations:

Given:
1) y = -x + 3
2) x + y = 8

To solve this system by graphing:
1) Graph the line y = -x + 3, which passes through the points (0,3) and (3,0).
2) Graph the line x + y = 8:
Rearranging the equation to y = -x + 8, we see that this line passes through the points (0,8) and (8,0).

Upon inspection, it can be observed that these two lines are parallel and will not intersect at any point on the graph. Therefore, there is no solution to the system of equations. The initial statement is correct:

"there is no solution to the system." - True