A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The equation of the solid line is y equals negative x plus 3. The equation of the dashed line is x plus y equals 8.
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.
(1 point)
Responses
The statement is true, because the lines have an intersection point.
The statement is true, because the lines have an intersection point.
The statement is false, because the lines have an intersection point.
The statement is false, because the lines have an intersection point.
The statement is false, because the lines are parallel.
The statement is false, because the lines are parallel.
The statement is true, because the lines are parallel.
1 answer
The statement is true, because the lines are parallel.
To explain: The equation of the solid line \( y = -x + 3 \) has a slope of -1, while the equation of the dashed line \( x + y = 8 \) can be rearranged to \( y = -x + 8 \), which also has a slope of -1. Since they have the same slope and different y-intercepts (3 for the solid line and 8 for the dashed line), these lines are indeed parallel and will never intersect. Therefore, there is no solution to the system.
