Question

Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution.
2x−3y=6
4x−6y=18

Answer 1

how do i start?

Answer 2

Okay 2 ways, the graphical method: which is just to arrange both equations to the subject of y. meaning 2x-3y=6 becomes y= (2/3)x -2 and so on...
then typing both equations into the GC, see if the 2 lines intersect, if it doesnt that means there are no solutions.

The 2nd way is just to solve the 2 equations.

2x−3y=6 => y = (2x-6)/3
4x−6y=18 => y= (4x-18)/6
Equating both eqn tgt

(2x-6)/3 = (4x-18)/6
4x-12 = 4x- 18
-12= -18

Which is a contradiction, so since there are no values of x that can fit into the eqn, there is no solution

Answer 3

can you just explain to me why did you put 2/3x-2?

Answer 4

Oh that also means y = (2x-6)/3, i just simplified it. sry for the confusion

Answer 5

thank you! i was like waiit a minute that makes no sense