X+y=8

Question

Y=-x-3

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)

The statement is false, because the lines have an intersection point.

The statement is true, because the lines have an intersection point.

The statement is true, because the lines are parallel.

The statement is false, because the lines are parallel.

Answer 1

To determine whether the statement is true or false, we can analyze the two equations given:

1. \( x + y = 8 \)
2. \( y = -x - 3 \)

Let's first rewrite the equations in slope-intercept form (if they aren't already):

1. From \( x + y = 8 \), rearranging gives: \[ y = -x + 8 \] This line has a slope of -1 and a y-intercept of 8.

2. The second equation \( y = -x - 3 \) is already in slope-intercept form, with a slope of -1 and a y-intercept of -3.

Now we can compare the two lines:

• Both equations have the same slope (-1), which means they are parallel.
• Since they have different y-intercepts (8 and -3), they will never intersect.

Because the two lines are parallel and do not intersect, there is no solution to the system.

Given this analysis, we can conclude that the correct statement is:

The statement is true, because the lines are parallel.