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
A. The statement is true, because the lines have an intersection point.
B. The statement is false, because the lines have an intersection point.
C. The statement is false, because the lines are parallel.
D. The statement is true, because the lines are parallel.
C. The statement is false, because the lines are parallel.
Solving the system y = -x + 3 and x + y = 8 algebraically:
From equation 2, we can isolate y:
y = 8 - x
Now we can substitute this value of y into equation 1:
8 - x = -x + 3
Simplifying:
8 = 3
This is not possible, as 8 does not equal 3. Therefore, there is no solution to the system.
By graphing the equations, we can show that the lines are parallel and do not intersect. Hence, option C is correct.