GREAT REWARD if you help me with equations.?

Question

Explain to me how an equation system works.
For example, I dont get :

5x+4y=53
6x+3y=64

It would be nice if you gave your own example too, because I just made that similar to my problem. Thanks!!!!!!! PLEASE EXPLAIN!!!!

Answer 1

when u have two equations like that, solve for one variable first (lets say y). then u plug the y equation into the second equation to solve for x. now u have a number. use the x value in the y equation.
example:
2y + 3x = 20
4y + x = 10

pick an equation and solve for a variable
4y + x = 10
x = -4y + 10
now use that equation in the other
2y + 3x = 20
2y + 3(-4y + 10) = 20
2y - 12y + 30 = 20
-10y + 30 = 20
-10y = -10
y = 1
plug y into x = -4y + 10
x = -4(1) + 10
x = -4 + 10
x = 6

Answer 2

When you have systems of equations you want to get the system down to a point where you can solve or eliminate one of the variables.

That way you can solve the system for the other varibles.

There are a bunch of ways to get rid of one of the variables. I'll go over the most used methods:

1. Multiplying equations by constants
2. Adding/ substracting equations
3. Substitution

The variable I'll be getting rid of is x, but you can use y if you want.

5x + 4y = 53
6x+ 3y = 64

1. If I multiply the first equation by 6 I get
30x + 24y = 318

Then if I multiply the second equation by -5 I get
-30x -15y = -320

So they look like this:
30x + 24y = 318
-30x-15y = -320

If I add the two equations together I get:
9y = -2
y = -2/9.

Putting y = -2/9 back into the equation, you get

6x -(2/3) =64

x = 97/9.

I actually did all 3 methods in the 1st problem. Here's a few simple problems to see the other methods.

Adding/ Subtracting equations

ex. 1

x + y = 10
9x -y = 20

You could solve for one variable and do a lot of algebra, but if you look at the equations carefully you can see if you add the two equations.

10x + 0 = 30. x=3.

So:
27 - y = 20.
y = 7.

Substitution example: basically you do algebra and get 1 variable and then put the equation for 1 variable in the other equations (not the one that you started with). I hope it's clearer with an example.

x -2y = 10
x + 5y = 30

Solving the first equation for 1 variable:
x = 10 + 2y

Putting this into the second equation

(10 + 2y) + 5y = 30

Then

7y+ 10 = 30
y = 20/7.

Doing this process for x you get x = 110/7.

Answer 3

Through performing addition, subtraction, multiplying, and division on the equations, variables are canceled out.

Multiply the 1st equation by 3:
15x+12y = 159
Multiply the 2nd equation by 4:
24x+12y = 256
As you can see, the y coefficient (12) for both of the equations is the same. Take the 2nd equation and subtract the 1st equation:
24x+12y-15x-12y = 256-159
9x = 97
x = 97/9

Putting x into the original 1st equation:
5(97/9)+4y = 53
485/9+4y = 53
4y = -8/9
y = -2/9

Answer 4

a system of equations is where the same ordered pair works for all the equations. you can solve them by two basic wats, substitution or elimination. substitution is when you solve for one of the variables in one equation, and plug it in to the other. like in your problem, solve for x by subtracting 4y from both sides then dividing both sides by 5. this should give you -4y/5+53/5=x. then you would plug in 4y/5+53/5 for your x variable in your second equation: 6(4y/5+53/5)+3y=64. when you solve for y, you get a number. that is your answer for y. then you plug that back into your first equation and solve for x. as you can see, this becomes pretty messy at times, so i recommend using elimination.
you do this by making two of your variables the opposite of each other and then adding your equations together, eliminating one variable. lets take out the y in this system. to do this, you must make 3 and 4 be opposites of each other(12 and -12). so times the first equation by 3, and the bottom equation by -4, making two new equations: 15x+12y=159 and -24x-12y=-256. then combine your equations, making one equation: -9x=-97. x=97/9 add this into one of your origional equations and solve for y.

Answer 5

take one of the equations by itself and solve for one of the variables (we'll do y). For this problem the second one would be easier to start with:
6x + 3y = 64
3y = -6x + 64
y = -2x + 64/3
Plug y into the first equation:
5x + 4(-2x + 64/3) = 53
5x -8x + 84 = 53
-3x = -31
x = 31/3
then plug 31/3 in for x to get y:
y = -2x + 64/3
y= -2(31/3) + 64/3
y= 2/3

hope this helps!

Answer 6

It's easy to get how it works if you just put the equations in a real world situation.

So let your x's be apples
and let your y's be oranges

5 apples + 4 oranges = $53

(Very expensive fruit, the best)

and

6 apples + 3 oranges = $64

You are buying the fruit from the same store in both situations so you know the price of an apple or an orange is going to be the same in both equations. Also you know that to maintain the balance you can do anything you like to one side of an equation as long as you do exactly the same to the other side. It's like a see-saw. If you add weight to one side you need to add weight to the other to make the see saw balance. Also if you take weight off one end you need to take it off the other end to make it balance. It's the same with equations.

So for 6 apples + 3 oranges = 64
take off 3 oranges from both sides....
to give you
6 apples = 64 - 3 oranges

Now divide both sides by 6...
to give you
1 apple = (64 - 3 oranges) / 6
Multiply both sides by 5...
to give you
5 apples = (64 - 3 oranges) x 5/6

Now you' ve described the price of 5 apples in terms of oranges. Go back to your first equation 5 apples + 4 oranges = 53

We can now substitute the 5 apples with (64 - 3 oranges) x 5/6

so (64 - 3 oranges) x 5/6 + 4 oranges = 53

multiply both sides by 6/5 and you get

64 - 3 oranges + 4.8 oranges = 63.6

That is 64 + 1.8 oranges = 63.6

take 63.6 from both sides and you get

0.4 + 1.8 oranges = 0

Now take 0.4 from both sides

1.8 oranges = -0.4

divide both sides by 1.8
and you get 1 orange = -0.22

So clearly the shopkeeper is cleverly paying people to take the oranges away from him if they promise to buy his very expensive apples at the same time. Let's see what I mean...

Now we now the value of one orange we can put it straight into one of the equations.

6 apples + 3 (-0.22) = 64
which is
6 apples - 0.6666 = 64
take 0.66666 from both sides
to give
6 apples = 63.33
divide both sides by 6
to give
1 apple = 10.55

So the price of an apple x is $10.55 and the price of an orange is -$0.22.

Okay so it's an appaling example but I hope you get the picture!!!

Answer 7

its easy, what multiplied by 5 would give you something that you can add to something multiplied by 4 would give you so you can get 53

Answer 8

wats the reward? wink wink

Answer 9

NO CLUE !