Question

Does this have infinite solutions?

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

Answer 1

Well if you math up the linear equations to cancel out a factor, you would get 0=-30

Answer 2

So it would have no solution

Answer 3

so we can present the equation as -

4x+6y+12 = 0
=> 2x+3y+4 = 0


2x+3y-9 = 0

so 2x/2x = 1, 3y/3y = 1, however 4/-9 does not equal to 1.

Ratios of all corresponding coefficients should be equal for infinite solutions; not observed here. Hence this system does not have infinite solutions.

(However since x1/x2 = y1/y2, this system has only one solution.)

Answer 4

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Answer 5

ok cut the last line; this eqn has no solutions since lines are parallel due to same x-coefficient and y-coefficient;