Question

Which system has infinite solutions? A) 4x + 6y = -12
2x + 3y = 9
Which system has (-2, -2) as the solution? B) x - y = -2
3x - y = 0
Which system has (1, 3) as the solution? C) x - 4y = -8
2x - 3y = -16
Which system has no solutions? D) x + y = -4
-3x + 2y = 2

Which system has (-8, 0) as the solution? E) x + y = -1
4x + 4y = -4

Answer 1

2x+3y=9; because you multiply infinitely many ways,
x-y=-2; plug it in

Answer 2

A system will have infinitely many solns if the two equation are REALLY the same equation - that is, the same line. One equation is just a multiple of the other.

This is easy to see if you put both equations into y=mx+b form, because the equations will be identical.

Answer 3

A system has NO solutions if the two lines given by the equations are parallel - because then, then will never intersect, so there is NO point (x,y) that is on both lines.

This is easy to see if you put both equations into y=mx+b form, because the SLOPES will be the same, but with different y-intercepts.

OR, if you just go about solving by elimination, and you get something where the variables are gone and the equation is clearly FALSE, e.g., 0=5 (or something like that).

Answer 4

I'm not sure what you're talking about - I don't see that equation in any of these systems??

Your answer is one of the SYSTEMS of 2 equations - A, B, C or D. Not a single equation. I'm not sure where you are getting the equation you state above, because it isn't in any of these systems.

Answer 5

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

Answer 6

OK; yes. That's no solution.

Like I said: if you use elimination
4x + 6y = -12
(-2)(2x + 3y) = 9(-2)

4x + 6y = -12
-4x - 6y = -18
0=-30
That's false, so it's an inconsistent system - no solution.

Answer 7

Also, both lines have slope -2/3, but different y-intercepts. So they are parallel.