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
⇒ [tex]y = \frac{4}{3} x - 4[/tex] {In slope-intercept form} ......... (3)
And, - 12x + 9y = 10
⇒ 9y = 12x + 10
⇒ [tex]y = \frac{4}{3} x + \frac{10}{9}[/tex] {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
⇒ [tex]y = - \frac{3}{2} x + \frac{19}{2}[/tex] ........... (5)
And, 4x - 5y = 10
⇒ [tex]y = \frac{4}{5}x - 2[/tex] ........ (6)
So, from the equations (5) and (6) we can say that the straight lines are oblique (intersecting). (Answer)
