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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.
The statement is false, because the lines are parallel.
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Answer 1

The correct response is:

The statement is true, because the lines are parallel.

Explanation: The solid line given by the equation \( y = -x + 3 \) and the dashed line given by the equation \( x + y = 8 \) are both linear equations that represent straight lines on the coordinate plane. When simplified, the dashed line can be rewritten in slope-intercept form as \( y = -x + 8 \). The slopes of both lines are the same (-1), indicating that they are parallel. Since parallel lines do not intersect, there is no solution to the system of equations.