Question

solving the system y=-x+3and x+y=8 by graphing shows they there is no solution to the system. is this statement true or false explain.

a. the statement is false, bc the lines are parallel
b. the statement is true, bc the lines have an intersection point.
c. the statement is true, bc the lines are parallel
d. the statement is false because the lines have an intersection point.

Answer 1

[AI-generated answer — Bot GPT 3.5]

d. the statement is false because the lines have an intersection point.

When graphed, the first equation y = -x + 3 is a line with a y-intercept of 3 and a slope of -1.
The second equation x + y = 8 can be rewritten as y = -x + 8, which is a line with a y-intercept of 8 and a slope of -1.

Both lines have the same slope but different y-intercepts, which means they intersect at a single point. Therefore, there is a solution to the system of equations.