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you can use matrices?
to find x and y
4x + 8y = 16 3x + 6y = 9 givees x + 2y = 4 x + 2y = 3
4x + 8y = 16 => x+2y=4 3x + 6y = 9 => x+2y =3 they contradict to each other...
3x + 6y = 9=y=3/2-x/2 x=2n+1 y=1-n y=3-x/2
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.
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.
huh? I have no idea what your saying or what reading
they are // lines, and don't have intercept...
i meant they don't intercept with each other
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
Do you know what slope-intercept form is?
m= blah blah blah?
Not exactly... It's y=mx+b
So, your original question asked how to determine the number of solutions WITHOUT solving...
and how do i do that?
Start by isolating "y" in both equations.
4x + 8y = 16 8y+4x=16?
That's a good start. Now, subtract 4x on both sides.
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
8y+4x=16 -4x -4x
8y=-4x+16 <---- like this :)
and leave it like that?
Not just yet, we're almost done. Then, to get the y by itself, you can divide each piece by 8.
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
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.
okay i think i got it now, thank you figure.
So here's the other equation: 3x + 6y = 9
You got it? Excellent! :)
yes, since your the only 1 out of 100 people that make sinces lol
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. :)
Thank you, though - of course.
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.
That's excellent! I bet that feels great!
you dont even know. lol
if you like all the work TheFigure did then you should thank him by pressing the 'Good Answer' button.