Question

given the equation -3x +2y =4, Write another equation that will form a linear system with:
one solution, no solution and infinite solution.


infinite solution:

(-3x +2y =) * 3 -> -9x +6y =12

y=3/2x+4
-9x +6y =12


I think we have to multiple the first equation by non-zero number right? But when I rewrite this -9x +6y =12 into slope-intercept form . it doesn't have to same answer as the original.

Answer 1

One Solution: Add to verify.
-3x + 2y = 4
3x + 2y = 4

No Solution: Multiply Eq1 by (-1) and add.
-3x + 2y = 4
-3x + 2y = 6

Infinite Solutions: Multiply Eq1 by 3 and compare.
-3x + 2y = 4
-9x + 6y = 12