anonymous
  • anonymous
How many solutions does the following system have: 4x + 8y = 16 3x + 6y = 9 Explain how to determine the number of solutions without solving the system. Then apply elimination, and interpret the resulting expression.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
x=2n y=2-n
anonymous
  • anonymous
you can use matrices?
anonymous
  • anonymous
to find x and y

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More answers

anonymous
  • anonymous
elimination
Zarkon
  • Zarkon
4x + 8y = 16 3x + 6y = 9 givees x + 2y = 4 x + 2y = 3
Callisto
  • Callisto
4x + 8y = 16 => x+2y=4 3x + 6y = 9 => x+2y =3 they contradict to each other...
anonymous
  • anonymous
3x + 6y = 9=y=3/2-x/2 x=2n+1 y=1-n y=3-x/2
anonymous
  • anonymous
I'd say put them both into slope intercept form and examine the slopes. If the slopes are different, there is only one solution. If the slopes are the same, examine the vertical intercepts. If the intercepts are the same it has infinitely many solutions, if the intercepts are different it has no solutions.
anonymous
  • anonymous
Without having too much imagination, let the first equation be (1) and the second one (2). Modify the forms in the following way: Let (1)* be (1) divided by four. Let (2)* be (2) divided by three. Combine by subtraction, so (1)*-(2)* gives 0 = 1. This contradiction tells us that the system is inconsistent, and there is no solution.
anonymous
  • anonymous
huh? I have no idea what your saying or what reading
Callisto
  • Callisto
they are // lines, and don't have intercept...
Callisto
  • Callisto
i meant they don't intercept with each other
anonymous
  • anonymous
i know that, i jut don't understand what I'm suppose to do with the equations everyone else is showing work? but this is the only problem i need help with and dont understand
anonymous
  • anonymous
Do you know what slope-intercept form is?
anonymous
  • anonymous
m= blah blah blah?
anonymous
  • anonymous
Not exactly... It's y=mx+b
anonymous
  • anonymous
|dw:1332637580537:dw|
anonymous
  • anonymous
oh,
anonymous
  • anonymous
So, your original question asked how to determine the number of solutions WITHOUT solving...
anonymous
  • anonymous
and how do i do that?
anonymous
  • anonymous
Start by isolating "y" in both equations.
anonymous
  • anonymous
4x + 8y = 16 8y+4x=16?
anonymous
  • anonymous
That's a good start. Now, subtract 4x on both sides.
Callisto
  • Callisto
normally, you'll solve the equation . but when you reduce the equation and find that the slope of the 2 equations is the same. Then you'll have 2 cases, first, then the y-int are not the same, they have no interception point, like this;|dw:1332565127626:dw|If they have the same slope and same y-int, they are of the same line and the equations have infinitely many solutions, like this|dw:1332565207097:dw| To find the slope and x/y-intercepts you can consider the general form: ax+by+c=0 slope = -a/b x-int = -c/a y-int = -c/b
anonymous
  • anonymous
y+4x=4?
anonymous
  • anonymous
8y+4x=16 -4x -4x
anonymous
  • anonymous
ooo
anonymous
  • anonymous
8y=-4x+16 <---- like this :)
anonymous
  • anonymous
and leave it like that?
anonymous
  • anonymous
Not just yet, we're almost done. Then, to get the y by itself, you can divide each piece by 8.
anonymous
  • anonymous
16/8?
anonymous
  • anonymous
8y=-4x+16 When you divide all 3 terms by 8, you should end up with: y=-4/8x+16/8 Then you can simplify: y=-1/2x+2
anonymous
  • anonymous
Now, we're going to write that down somewhere and do the same thing we did to this equation to the other equation. Then we will compare the two.
anonymous
  • anonymous
okay i think i got it now, thank you figure.
anonymous
  • anonymous
So here's the other equation: 3x + 6y = 9
anonymous
  • anonymous
You got it? Excellent! :)
anonymous
  • anonymous
You're welcome!!
anonymous
  • anonymous
yes, since your the only 1 out of 100 people that make sinces lol
anonymous
  • anonymous
Well, to be fair to the others, they aren't wrong. They're just explaining it at a level that I'm not sure you're ready for just yet. You'll get there though. :)
anonymous
  • anonymous
Thank you, though - of course.
anonymous
  • anonymous
lol i know that, I've never done math higher than pre algebra, I already failed college math 2 times and this is my second and im actually passing with in 2 weeks finally.
anonymous
  • anonymous
lol.
anonymous
  • anonymous
That's excellent! I bet that feels great!
anonymous
  • anonymous
you dont even know. lol
Zarkon
  • Zarkon
if you like all the work TheFigure did then you should thank him by pressing the 'Good Answer' button.

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