Question

For the systems of linear equation in question: x/3-y/5=4 and 3x/4+2y/3=6. Determine how many solutions exist, use either elimination or substitution to find the solutions (if any), graph the two lines, labeling the x-intercepts, y-intercepts, and points of intersection.

Answer 1

x=174/34 & y=-450/37 by sub.. method

Answer 2

I recommend solving both equations for y first.

Answer 3

well, i actually got the x-intercept and the y-intercept... but its in fraction

Answer 4

You really don't need an x or y-intercept to solve this

Answer 5

i got x = 696/67 and y = -180/67

Answer 6

i don't

Answer 7

Nope.....I will show you the first few steps

Answer 8

cool

Answer 9

Okay, the steps are a bit more than what you may like, but this is truly the proper way to do it....

Answer 10

x=174/34 & y=-450/37 i guess this is the answer...

Answer 11

Akshay, how would I graph it?

Answer 12

\[\frac {x}{3} - \frac{y}{5} = 4\]

Add y/5 to both sides:
\[\frac {x}{3} = 4 + \frac {y}{5} \]

Subtract 4 from both sides:
\[\frac {x}{3} - 4 = \frac{y}{5}\]

Multiply both sides by 5:
\[5(\frac {x}{3} - 4) = y\]

Simplify to get:
\[y = \frac{5x}{3} - 20\]

Answer 13

That seems like a bit much, but if you do the same thing with the other equation you end up with: \[y = 9 - \frac{9x}{8}\]

Answer 14

Now if you set the equations equal to each other you will have:

y = y

Answer 15

Now substitute the two equations in for y:

\[\frac{5x}{3} - 20 = 9 - \frac{9x}{8} \]

Answer 16

Now you have something a little easier to work with..... You can just solve for x from there...

Answer 17

ok, i think i get it...

Answer 18

\[ x = \frac{696}{67} \approx 10.3881\]

Answer 19

i'm trying to understand how you got y=9-9x/8

Answer 20

yeah, that's what i got...

Answer 21

That's what the the other equation becomes when you solve for y. You posted two equations

Answer 22

yeah, i posted 2 equations... but how would I graph it, cause the website that my professor issued us, it won't allow me to put in the decimal

Answer 23

As a matter of fact, now that I think of it, I better way to solve for y would have been to multiply by factors to get rid of the denominators

Answer 24

ok, nvm.., got it

Answer 25

To graph it....I'll give you a link to a program you can use to graph it

Answer 26

cool

Answer 27

http://www.geogebra.org/webstart/4.0/geogebra-40.jnlp

Answer 28

That's geogebra....or you can just use wolfram alpha.... http://www.wolframalpha.com/

Answer 29

Either way...

Answer 30

I personally prefer geogebra because it has CAS and many other features

Answer 31

cool

Answer 32

thanks

Answer 33

You're most welcome

Answer 34

By the way, when you're graphing this, here are the equations you should enter:
y=9-(9x)/(8)
y = (5x)/(3) - 20

And then the graph will give the intersection points

Answer 35

cool

Answer 36

If you solve for y for both equations, then set them equal to each other, you will always get it correct. The other two didn't get it right because the substitution method they use doesn't always yield a correct result. The way I've shown you produces a correct result if there is indeed a solution.