Question

solve each system using substitution.
3x+2y=23
1/2x-4=y

Answer 1

help please i have been stuck for hours

Answer 2

@Luigi0210

Answer 3

Substitute y from 2nd equation to 1st equation

\[3x + 2(\frac{1}{2x}-4) = 23\]

\[3x + \frac{1}{x} = 31\]

\[3x^2 - 31x + 1 = 0\]
Solve it then you have \[\Delta = 31^2 - 4*3 = 949\]
So \[x_{1,2} = \frac{31 \pm \sqrt{949}}{6}\]

You can let it be or approximate

For me, I prefer to approximate results,
\[x_{1} \approx 10.3 \] and \[x_{2} \approx 0.032\]

Substitute then you can calculate y_1 and y_2 by yourself

Answer 4

I think you made a mistake there xD

Answer 5

Now I can see you reply Luigi..

Answer 6

oh wow thats a completely different way than what i was taught

Answer 7

Yeah, it's unclear whether that is
\[\frac{1}{2}x\]or\[\frac{1}{2x}\]

Answer 8

Sorry, when someone else is answering, it's polite to wait till they're done. :)

Answer 9

its \[\frac{ 1 }{ 2 }x \]

Answer 10

ok

Answer 11

It's good to see you again @whpalmer4 :)

Answer 12

Well, I would do

\[3x+2y=23\]\[3x+2(\frac{1}{2}x-4) = 23\]\[3x+x-8=23\]and I think you can see the rest of the way, right?

Answer 13

@luigi0210 backatcha :-)

Answer 14

i got up to there but then i got stuck

Answer 15

He's got you~

Answer 16

Well, collect like terms...

Answer 17

ok so \[4x-8=23\]

Answer 18

Okay, add 8 to both sides

Answer 19

and subtract 8 from both sides so you have 4=31 but then what it dosent work

Answer 20

i mean add

Answer 21

\[4x-8+8=23+8\]\[4x=31\]Now divide both sides by 4

Answer 22

Yeah, you get an unattractive-looking fraction, but that's the right answer for the problem you posted...

Answer 23

ok thanks

Answer 24

then use the value you get for \(x\) to find the value of \(y\) (also una brutta figura, as it turns out)