## ValentinaT Group Title Help with solving systems of equations? Solve using two different methods. Explain which method you found to be more efficient. a. 3x – 9y = 3 6x – 3y = -24 one year ago one year ago

1. ValentinaT Group Title

2. oadmhernandez Group Title

i like the addition method... 3x-9y=3, multiply this equation x -2 6x-3y=-24 -2(3x-9y=3), now becomes -6x+18y=-6 now, add/sub -6x+18y=-6 6x-3y=-3 0x+15y=-9 15y=-9 y=-9/15 y=-3/5

3. oadmhernandez Group Title

now, plug in y=-3/5 into 3x-9y=3 and solve for x. 3x-9(-3/5)=3 3x+27/5 = 3, lets get rid of the fraction 27/5 by multiplying everything x 5. 5(3x+27/5=3) 15x+27=15 15x=-12 x=-12/15 x=-3/5

4. MathDad72 Group Title

Are you good? Just got your message.

5. ValentinaT Group Title

I'm a bit confused, I thought the three ways of solving systems, are substitution, elimination, or graphing...?

6. oadmhernandez Group Title

A system of linear equations can be solved four different ways: Substitution Gaussian Elimination Matrices Graphing

7. oadmhernandez Group Title

what I showed you is the subsitution method... please disregard "Addition Medthod"... that is incorrect.

8. ValentinaT Group Title

Okay, thank you. If you don't mind could you also show me one of the other methods of solving this equation?

9. heredia7 Group Title

The equation is $3x - 9y = 3$ To simplify the equation, you must isolate both variables. I am going to start with trying to isolate the variable $x$ To do that, I divide $3x$ by 3 If you divide one side of the equation by 3, you have to do the same to the other side. $\frac{ 3x } {3} - 9y = \frac{ 3 }{ 3 }$ The 3's on the left side cancel each other out so you are left with $x - 9y = \frac{ 3 }{ 3 }$ On the right,$\frac{ 3 }{ 3 } = 1$ The result is$x - 9y = 1$ Now, I have to isolate the variable y $x-\frac{ 9y }{ 9 } = \frac{ 1 }{ 9 }$ On the left, the 9's cancel each other out so your are left with$x - y = \frac{ 1 }{ 9 }$ To simplify 1/9 is up to you.

10. ValentinaT Group Title

11. MathDad72 Group Title

@ValentinaT Here, kids were little turds getting to bed

12. MathDad72 Group Title

I will go over a few things like we did last time. Let's work on the first equation: 3x-9y=3, solve it for one of the variables. Lets solve it for x. So add 9y to each side and we will get 3x=9y+3. Now divide each side by 3 and we will get x=3y+1. So now we will put the x=3y +1 into 6x-3y=-24. So we will have 6(3y+1)-3y=-24. Multiply it out and get 18y+6-3y=-24. Which becomes 15y+6=-24. Next step is subtract 6 from each side and get 15y=-30. Finally divide each side by 15 and get y=-2. Now we know what y is equal to -2 we can put that into either original equation or the one where we solved x=3y+1. If we do the later one we will get x=3(-2)+1. Then x=-5. If we put them back into an original equation we will get 3(-5)-9(-2)=3 -15+18=3 3=3. And we are good. I hope this helped email me or send a message if you have any questions.

13. MathDad72 Group Title

So with the elimination method we want to manipulate one equation so that when we add the two equations together one will cancel out. We have: 3x-9y=3 6x-3y=24 we can do one of several things to work this out. First we could multiply the top row by (-2) and get: -6x+18y=-6 Bottom stays the same: 6x-3y=-24 Adding we get: 15y=-30 Divide each side by 15 and get: y=-2 Plug 2 back into one of the original and solve for your x value: 3x-9(-2)=3 3x+18=3 3x=-15 x=-5 Se we again get our X=-5 and y=-2 NOTE: We could have multiplied the bottom row with a (-3) and get: Top row stays the same: 3x-9y=3 -18x+9y=72 Add them and get: -15x=75 so x=-5 Plug the -5 back into one of the original and get: 3(-5)-9y=3 -15-9y=3 -9y=18 y=-2 And like magic we get the same numbers. Hope this helped.

14. ValentinaT Group Title

Thank you.