Use the image to answer the question.%0D%0A%0D%0A%0D%0A%0D%0ASolving 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. %0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0AThe statement is false, because the lines are parallel.%0D%0AThe statement is false, because the lines are parallel.%0D%0A%0D%0AThe statement is true, because the lines are parallel.%0D%0AThe statement is true, because the lines are parallel.%0D%0A%0D%0AThe statement is false, because the lines have an intersection point.%0D%0AThe statement is false, because the lines have an intersection point.%0D%0A%0D%0AThe statement is true, because the lines have an intersection point.%0D%0AThe statement is true, because the lines have an intersection point.%0D%0ASkip to navigation%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A%0D%0AHighlight%0D%0AItem%0D%0A1%0D%0A, Unattempted.%0D%0AItem%0D%0A2%0D%0A, Unattempted.%0D%0AItem%0D%0A3%0D%0A, Unattempted.%0D%0AItem%0D%0A4%0D%0A, Unattempted.%0D%0AItem%0D%0A5%0D%0A, Unattempted.%0D%0APreviousNext

Question

Use the image to answer the question.%0D%0A%0D%0A%0D%0A%0D%0ASolving 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. %0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0AThe statement is false, because the lines are parallel.%0D%0AThe statement is false, because the lines are parallel.%0D%0A%0D%0AThe statement is true, because the lines are parallel.%0D%0AThe statement is true, because the lines are parallel.%0D%0A%0D%0AThe statement is false, because the lines have an intersection point.%0D%0AThe statement is false, because the lines have an intersection point.%0D%0A%0D%0AThe statement is true, because the lines have an intersection point.%0D%0AThe statement is true, because the lines have an intersection point.%0D%0ASkip to navigation%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A%0D%0AHighlight%0D%0AItem%0D%0A1%0D%0A, Unattempted.%0D%0AItem%0D%0A2%0D%0A, Unattempted.%0D%0AItem%0D%0A3%0D%0A, Unattempted.%0D%0AItem%0D%0A4%0D%0A, Unattempted.%0D%0AItem%0D%0A5%0D%0A, Unattempted.%0D%0APreviousNext

Answer 1

The statement is true, because the lines have an intersection point. By graphing the two equations, y = -x + 3 and x + y = 8, we can see that the two lines intersect at the point (2,6). Therefore, there is a solution to the system of equations.

Answer 2

The statement is true because the lines have an intersection point. If we graph the two equations y = -x + 3 and x + y = 8, we can see that the lines intersect at the point (2, 6). Therefore, there is a solution to the system.

Answer 3

To determine if the statement is true or false, we need to analyze the given system of equations and how they are graphed.

The first equation is y = -x + 3, which is a linear equation in slope-intercept form. The slope of this line is -1, and the y-intercept is 3. This means the line starts at the point (0, 3) and has a slope of -1, indicating it goes downwards from left to right.

The second equation is x + y = 8, which can be rewritten as y = -x + 8. This is another linear equation in slope-intercept form. The slope of this line is also -1, and the y-intercept is 8. This line starts at the point (0, 8) and also has a downward slope.

To graph these two lines, plot the y-intercepts (0, 3) and (0, 8) on the y-axis. Then, using the slope of -1, move 1 unit to the right and 1 unit down from each intercept to find additional points on the lines. Connect these points with a straight line.

Upon graphing, you will notice that the two lines are parallel, meaning they do not intersect at any point. Therefore, there is no solution to the system of equations.

Therefore, the correct answer is: The statement is true, because the lines are parallel.