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

The correct response is:

The statement is true, because the lines are parallel.

Explanation: The equation of the solid line is \( y = -x + 3 \) and the equation of the dashed line is \( x + y = 8 \). To check if the lines are parallel, we can express both lines in slope-intercept form (y = mx + b) and compare their slopes.

1. The solid line \( y = -x + 3 \) has a slope of -1.
2. Rearranging the dashed line \( x + y = 8 \) gives \( y = -x + 8 \), which also has a slope of -1.

Since both lines have the same slope (-1), they are parallel. Since parallel lines never intersect, the system of equations has no solution, confirming the original statement is true.