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 have an intersection point.
The statement is false, 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.
3 answers
The statement is true, because the lines are parallel.
The solid line \( y = -x + 3 \) has a slope of -1, while the dashed line \( x + y = 8 \) can be rewritten as \( y = -x + 8 \), which also has a slope of -1. Since both lines have the same slope but different y-intercepts (3 for the solid line and 8 for the dashed line), they are parallel and will never intersect, indicating that there is no solution to the system of equations.
Based on the answer choices provided, the correct response is:
The statement is true, because the lines are parallel.
This accurately reflects that the lines do not intersect, confirming that there is no solution to the system of equations.
3 answers
1 answer
1 answer
1 answer