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ValentinaT

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
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  1. ValentinaT
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    • one year ago
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  2. oadmhernandez
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    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

    • one year ago
  3. oadmhernandez
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    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

    • one year ago
  4. MathDad72
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    Are you good? Just got your message.

    • one year ago
  5. ValentinaT
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    I'm a bit confused, I thought the three ways of solving systems, are substitution, elimination, or graphing...?

    • one year ago
  6. oadmhernandez
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    A system of linear equations can be solved four different ways: Substitution Gaussian Elimination Matrices Graphing

    • one year ago
  7. oadmhernandez
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    what I showed you is the subsitution method... please disregard "Addition Medthod"... that is incorrect.

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

    • one year ago
  9. heredia7
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    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.

    • one year ago
  10. ValentinaT
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    @MathDad72 ?

    • one year ago
  11. MathDad72
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    @ValentinaT Here, kids were little turds getting to bed

    • one year ago
  12. MathDad72
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    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.

    • one year ago
  13. MathDad72
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    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.

    • one year ago
  14. ValentinaT
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    Thank you.

    • one year ago
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