Question 11

x + 2y = 8 and -x - 2y = 3 represent parallel lines.

The equations x + 2y = 8 and -x - 2y = 3 represent parallel lines because they have the same slope when expressed in slope-intercept form. This indicates that their lines will never intersect.

A) -2x + y + 2 = 0, y = -(1/2)x - 4

This pair of equations does not represent parallel lines because the first equation can be rewritten in slope-intercept form as y = 2x - 2, which has a slope of 2, while the second equation has a slope of -1/2. Since their slopes are different, these lines will intersect.

B) 3x + y = -8, y = 3x - 8

These equations do not represent parallel lines. The first equation can be rearranged to y = -3x - 8, which has a slope of -3. The second equation has a slope of 3. Because their slopes are not equal, these lines will intersect.

C) x + 2y = 8, -x - 2y = 3

This pair of equations represents parallel lines. Both equations can be expressed in slope-intercept form, revealing that they share the same slope of -1/2. Therefore, as they have identical slopes, these lines will never intersect.

D) -(2/3)x + y = 12, y = -(3/2)x - 1

These equations do not represent parallel lines. The first equation can be rearranged to the slope-intercept form y = (2/3)x + 12, giving it a slope of 2/3. The second equation has a slope of -3/2. Since their slopes differ, these lines will intersect.

Conclusion

The equations x + 2y = 8 and -x - 2y = 3 are the only pair among the options that have the same slope, confirming that they are parallel lines. The other options feature different slopes, which indicates that those lines will intersect rather than remain parallel.