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Question
Use the image to answer the question.
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 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.
The statement is true, because the lines have an intersection point.
The statement is false, because the lines are parallel.
1 answer
The statement is true, because the lines are parallel.
When two lines are parallel, they never intersect. In this case, the solid line represented by the equation \(y = -x + 3\) and the dashed line represented by the equation \(x + y = 8\) are parallel to each other, which means they do not have any points of intersection. Therefore, the system of equations has no solution.
