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 false, because the lines are parallel.
The statement is false, because the lines are parallel.
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 true, because the lines are parallel.
The statement is true, because the lines are parallel.
The statement is true, because the lines have an intersection point.
1 answer
The correct response is:
The statement is true, because the lines are parallel.
Explanation: The solid line's equation \(y = -x + 3\) has a slope of \(-1\), while the dashed line's equation \(x + y = 8\) can be rearranged to \(y = -x + 8\), which also has a slope of \(-1\). Since both lines have the same slope and different y-intercepts (3 and 8, respectively), they are parallel and will never intersect. Therefore, the system has no solution.
