Question

Are these collinear(coincident), parallel, perpendicular, oblique(intersecting)

Answer 1

Answer:

1. Collinear

2. Parallel

3. Oblique

Step-by-step explanation:

1. The system of linear two variable equations are  

3x - 2y = 2 ........... (1) and  

6x - 4y = 4, ⇒ 3x - 2y = 2 ........... (2) {Dividing both sides with 2}

So, equations (1) and (2) are identical.  

Therefore, the lines are collinear. (Answer)

2. The system of linear two variable equations are  

4x - 3y = 12  

⇒ 3y = 4 x - 12

⇒ $y = \frac{4}{3} x - 4$ {In slope-intercept form} ......... (3)

And, - 12x + 9y = 10

⇒ 9y = 12x + 10

⇒ $y = \frac{4}{3} x + \frac{10}{9}$ {In slope-intercept form} .......... (4)

Since, equation (3) and (4) has the same slope, so, they are parallel. (Answer)

3. The system of linear two variable equations are  

3x + 2y = 19

⇒ $y = - \frac{3}{2} x + \frac{19}{2}$ ........... (5)

And, 4x - 5y = 10

⇒ $y = \frac{4}{5}x - 2$ ........ (6)

So, from the equations (5) and (6) we can say that the straight lines are oblique (intersecting). (Answer)