SOLUTION: I am very desperate here and have no clue were to turn. I am a single mother of 3 45 yrs old whom went back to college and now feel really stupid. I am forced to take this course

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Question 914249: I am very desperate here and have no clue were to turn. I am a single mother of 3 45 yrs old whom went back to college and now feel really stupid. I am forced to take this course as part of my goals to obtain my degree. Were doing solving systems of linear equations by substitution and i have no clue how to do it i have worked countless hours on this and many other chapters and just can't get it and i have to complete three chapters by the 21st for my midterm grade if not i'm going to just have to crush my dreams by dropping out of college and looking like a failure to my kids. the question is: Solve the following system of linear equations by substitution:
{-2x+y=24
{5y =10x+120
These are all in one bracket not two i have no clue how to make it just one bracket. Then under it say's please select whether the given system of linear equations is consistent, inconsistent, or dependent. if the system is consistent, please enter the solution.
Thank you so much for helping me and others out there.
Rebecca
Found 4 solutions by jim_thompson5910, lwsshak3, mananth, ankor@dixie-net.com:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
First solve for y. So isolate y.



add 2x to both sides

Now that y is fully isolated, we plug this into the second equation. This is where the term "substitution" comes from. We substitute y for 2x+24





replace EVERY copy of y with 2x+24

Now we have eliminated every copy of y. We can now solve for x.

Start with the given equation.


Distribute.


Subtract from both sides.


Subtract from both sides.


Combine like terms on the left side.


Combine like terms on the right side.


Simplify.


Since this equation is ALWAYS true for any x value, this means x can equal any number. So there are an infinite number of solutions.

So there are infinitely many solutions for this system.

This means that the system is dependent (one equation "depends" on the other; I like to think of it as one line leaning on the other)

Graphically, these 2 equations form the same line. One line lies perfectly on top of the other. This results in infinitely many intersections (recall that an intersection visually corresponds to a solution).

Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at jim_thompson5910@hotmail.com
or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html

Thanks,

Jim
Answer by lwsshak3(11628)   (Show Source): You can put this solution on YOUR website!
Solve the following system of linear equations by substitution:
{-2x+y=24
{5y =10x+120
***
-2x+y=24
y=24+2x
plug in 24+2x for y in 2nd equation and solve for x
5y =10x+120
5(24+2x)=10x+120
120+10x=10x+120
lines coincide
system is consistent and equations are dependent
system has infinitely many solutions
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
-2x+y=24
5y =10x+120

The brackets just indicate that they are a set of equations. A linear system with two variables x & y

-2x+y=24
rearrange
y=2x+24
substitute y in the equation below
5y =10x+120
5(2x+24) =10x+120
10x+120= 10x+120
10x-10x=120-120
0=0
The solution of one equation satisfies the other equation.
Hence
The system is consistent and has innumerable or infinite solutions.
and dependent







Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
-2x + y = 24
:
5y = 10x + 120
Simplify this equation by dividing each term by 5, then you have
y = 2x + 24
we can rearrange it like the 1st equation (subtract 2x from both sides)
-2x + y = 24
Now we can see the two equations are equiv, so we call them dependent
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