solve the system of equations?

Question

using the addition (elimination) method. if the answer is a unique solution present it as an ordered pair (x.y) if not specify wether the answer is "no solution" or "many solutions"
3x - 2y = 7
-9x + 6y = -21

Answer 1

3(3x-2y=7) = 9x-6y=21
-9+6y=-21

answer is 0=0

you can tell that it is the same line because the answer is 0=0 (many solution)
if it was 5=3 or something like that, it means that it is parallel (no answer)

Answer 2

OK... first you gotta set the equation to eliminate one of the variables. I will eliminate the y on top. To do this you must multiply the top equation by -3 in order to get the y to cancel out:

-3 (3x-2y=7) --------------- -9x+6y= - 21
-9x+6y=-21 --------------- -9x+6y= -21

Now once you do that you realize that the top and the bottom equation is the same which means that the solution is "many Solutions"

Answer 3

Multiply 1st equation by 3 getting:
9x -6y =21
Add 2nd equation getting 0 = 0
Thus the two equations are the same lineand there are many solutions.

Answer 4

if you multiply the 1st equation by -3, you get the 2nd equation. so if you graphed them both, you'd see just 1 line, each of the infinitely many points on the line is a solution.

if the 2nd equation ended with = something other than -21, you'd have 2 parallel lines, no common points, no solution.

Answer 5

(3x - 2y = 7 (3)
(-9x + 6y = -21

(9x - 6y = 21
(-9x + 6y = -21
-----------------
9x - 9x -6y + 6y = -21+21 = 0
no solutions
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Answer 6

You honestly can't see that one equation is -3 times the other?? And that means no unique solution??


Doug

Answer 7

many solutions