Linear Algebra Question Give a geometric description of the

Linear Algebra Question

Give a geometric description of the following system of equations. Your options for answers are listed below so please choose from the following:

Three identicle lines

A set of parallel lines

Three lines intersecting at a single point

Three non-parallel lines with no common intersection

(1 point) Give a geometric description of the following systems of equations Select Answer +y= 23x - 3y-11 Select Answer +y= 7 233y -14 23x - 3y-14 Select Answer 3. 416 y 16y = 4 -728y --7

Solution

!. The lines x + y = 7 , -6x + y = 1 and -23x - 3y = 14 are three non- parallel lines with no common intersection. The slopes of the three lines are all different so that these lines are not parallel. The first two lines meet at ( -8/5, 43/5) which is also on the 3rd line.Thus, the given three lines meet at the point ( - 8/5, 43/5)

2. x + y = 7, -6x -y = 1 and -23x - 3y = 14 are three non- parallel lines with no common intersection. The slopes of the three lines are all different so that these lines are not parallel. The first two lines meet at ( -8/5, 43/5) which is not on the 3rd line.Thus the three given lines are non - parallel lines which do not have any common intersection.

3. 4x - 16 y = 4, 2x - 8y = 2 and - 7x + 28y = -7. If we divide both the sides of the 1st equation by 4, the 2nd equation by 2 and the 3rd equation by - 7, then the new equations are x - 4y = 1, x - 4y = 1 and x - 4y = 1 which are same. Therefore, these are three identical lines.