Determine which system below will produce infinitely many solutions.

-4x + 6y = 20
4x - 3y = -2

-2x + 4y = 18
4x - 8y = -36

3x - 2y = 5
-6x - 4y = -10

5x - 3y = 12
15x - 9y = 24

Question

Determine which system below will produce infinitely many solutions.

 -4x + 6y = 20
4x - 3y = -2

 -2x + 4y = 18
4x - 8y = -36

 3x - 2y = 5
-6x - 4y = -10

 5x - 3y = 12
15x - 9y = 24

campbell_st · Answer

for infinite solutions you need to look to see if 1 line is a multiple of the other...

so looking at the last pair

  5x - 3y =12
15x - 9y = 24

multiply the 1st equation by 3

 15x - 9y = 36

so what has happened here is that the likes are parallel... same coefficients of x and y, but a different intercept...1st line has a y intercept y = 4
                                            2nd line has a y intercept of y = 2 2/3

hope it helps