Question

2x-3y=9;3y-2x=6 solve the system of equations graphically. If the system does not have a singe ordered pair state whether the system is inconsistent or dependent

Answer 1

What are we doing here @micki1130 ???????

Answer 2

10


micki1130
2x-3y=9;3y-2x=6 solve the system of equations graphically. If the system does not have a singe ordered pair state whether the system is inconsistent or dependent

Answer 3

there are actually 3 ways you can solve this problem, graphing, substitution and elimination

Graphing:first put both equation into y=mx+b form
2x-3y=9 3y-2x=6
-3y=9-2x 3y=6+2x
y=-9/3+2/3x y=6/3+2/3x
y=2/3x-3 y=2/3x+2
you can already see that the lines will be parallel since they have the same slope and different y intercept but if you didn't pick up on that you would go ahead and put those into your graphing calculator and the that there is no intersection and this means the system is inconsistent.

Substitution:first solve one equation for either x or y (doesn't matter which one) I'll do x
2x-3y=9
2x=9+3y
x=9/2+3/2y

then substitute this x value into the second equation

3y-2(9/2+3/2y)=6
3y-9-3y=6
-9=6 ??? they're not equal so they're inconsistent

Elimination: Normally you will have to multiply the entirety of one of the equations to get on of the variables to cancel out but here you can see that they both cancel out. Then you line up the variables and add the 2 equations together
2x-3y=9 Ex.-3x+2y=9 -2(-3x+2y=9) 6x-4y=-18
-2x+3y=6 -5x+4y=17 _____> -5x+4y=7 ____>-5x+4y=17
____________ ___________ ______________ ____________
0x+0y=15 0x+1x=-1
1x=-1
x=-1
when both x and y cancel out, the equation states 0=15. since this is not possible, they equations are inconsistent. if both variables do not cancel out like in the example, plug the value back into either equation and solve for the opposite variable. you should get the same value out of both equations. together the x and y values give you your solution set.

-3(-1)+2y=9 -5(-1)+4y=17
3+2y=9 5+4y=17
2y=6 4y=12
y=3 y=3 Ex. solution set (-1,3) and dependent

sorry that was so long, but i think it will really help if you read through it all. Good luck!