Simultanious Questions?

Question

yes this is my homework if your wandering, but i dont understand a thing that comes out of my math teachers mouth, my mates dont either. help!!! anyway heres the question hope you can help me??
3x+2y=12
3x+y=9
find the value of x and y x please help me!!! thanx x

Answer 1

3x+2y=12
3x+y=9
(2)*-2
-6x-2y=-18
3x+2y=12
adding
-3x=-6
dividing by -3
x=2
sub x=2 in 3x+2y=12
6+2y=12
adding -6
2y=6
dividing by 2
y=3

Answer 2

These are called simultaneous equations because you are solving two different equations at the same time. There are several ways to find x and y but I will show you the easiest way.

3x + 2y = 12
3x + y = 9
You want to eliminate either x or y so that you get a single equation that you can solve. Can you see that if we subtract the second equation from the first equation we get
3x-3x +2y -y = 12-9?
This gives y = 3
Now stick y=3 into either of the two equations to get x.
Let's take the second equation to get:3x +3 =9
So 3x=6 and x=2

So just find a way to eliminate either x or y.

2x + 4y = 10
x + y = 3
In this case you would multiply the second equation by 2 to get:
2x + 2y = 6. Now you can subtract this new equation from the first equation and the x terms cancel out leaving you with
2y=4 so y=2
Since x+y=3 x =1

Hope this helps. There is nothing worse than a poor teacher.

Answer 3

For ease, we would refer to the two equations as equations (1) and (2) respectively

3x+2y=12 ... (1)
3x+y=9 ... (2)

First of all, to find x and y, we need 2 equations because there are 2 unknowns; x and y. If there is one unknown, we need only one equation to find it, likewise if there are 3 unknowns; x, y, z, we need 3 equations to solve it.

Now, we need to make one of the unknowns the subject of one equation and substitute it in the other to find the solutions. When an unknown is the subject of an equation, it means that unknown stands on one side of the equality sign.

3x+2y=12 ... (1)
3x+y=9 ... (2)

Looking at the two equations, in which one do you think that we can easily make an unknown (x or y) the subject. You are right! In equation (2) we can easily make y the subject of the equation because it already stands on it's own, it does not carry any co-efficients(whole numbers that stand in front of unknowns).

So making y the subject of the equation (2), we have:

y = 9 -3x ... (3)

When 3x crosses to the other side of the equality sign, it becomes -3x. We call this equation (3) for easey reference.

Now, substitute the value of y in (3) in equation (1). The rule here is, if you use equation (1) to get equation (3), then you MUST substitute in equation (2). Likewise, if you use (2) to get (3), you must substitute in (1). This is to make sure that both equations are used in finding the values of x and y.

Substituting in (1) we have:
3x+2(9 -3x) =12
3x + 18 - 6x = 12
3x - 6x = 12 - 18
-3x = -6
-3x/-3 = -6/-3
x = 2

Substitute the value of x in (3) as this is the only equation that has not been used.

y = 9 -3x
y = 9 - 3(2)
y = 9 - 6
y = 3

Therefore x = 2, y = 3

Check ...
To check that the answers are correct we substitute the values of x and y in equations (1) and (2)

3x+2y=12 ... (1)
3x+y=9 ... (2)

3(2) + 2(3) = 12 ... (1)
6 + 6 = 12
12 = 12!

3(2) + 3 = 9 ... (2)
6 + 3 = 9
9 = 9!

Answer 4

Right, I'm assuming you need to understand the basics of simultaneous equations as well as the method for solving them.

The most mportant thing to remember is that in both equations the X's equal each other, and the Y's equal each other.

first off you have to organise the equations so they hae one thing in common, ie an equal number of X's or an equal number of Y's

so:

3x+2y=12

3x+y=9

as you can see there are already equal nummber of X's, so you move onto the next step, subtract one equation from the other one.

3x+2y=12
-
3x+y=9

3x - 3x = 0
2y - y = y
12 - 9 = 3

so you end up with

y=3

to get X you simply substitue the real value of y back into the equation and rearrange it to get the value of X

3x + 2y = 12

becomes

3x + (2*3) = 12

3x + 6 = 12

take 6 from both sides of the equation

3x = 6

divide both sides by 3

x=2

and you're all done


x=2 and y=3

Answer 5

Simultaneous Equations is a way of eliminating the varibles

In this case to eliminate the x from the equations you take the first equation from the second one.

3x+2y=12
3x+y=9

Gives

3x+2y-3x-y=12-9

and so

y=3

Then you just substitue y=3 into a equation to give the value of x which is x=2

If you don't luckily have the same coefficients of x..ie the number in front, then you just have to take multiples of a equation.
If the x value on the 2nd equation was a negative then to eliminate it you add as 3x+ -3x gives 0.

Hoped that helped with this question and future ones.

Oz

Answer 6

3x is common to each equation. Don't let it scare you. Just call it a single entity "Threex"
Now: Threex + TWO Y's = 12
Threex + ONE Y = 9
The difference between having 1 0r 2 Y's is 3
So: Y=3
If 3x + 2x3 = 12
Then 3x + 6 = 12
Then 3x = 6
And x = 2

(You could add the two equations together and plug-in x = 2 and y = 3 into the resulting 6x + 3y = 21 as a check)

Answer 7

For simultaneous equations you have to get two terms so they are the same in both equations (here it's already done-3x) and then work out x and y (as shown below).

OK, so your simultaneous equations are:
3x+2y=12
3x+y=9

-First you must get two terms the sme-which has already been done for you (3x). So when you have this you minus the smaller equation from the bigger equation (for this particular example, if the signs were different, eg. + and - then you'd add the eqautions, but never mind that for this example).
-So it'd be (3x-3x) + (2y-y) = (12-9)
which would come to y=3. That's the first part of your answer.
-Now to work out x you must substitute your previous answer into one of the simultaneous equations (either one, easier to pick the simpler one).
I'll pick the 2nd equation (3x+y=9). So it's be 3x + 3 = 9. Now we minus 3 from both sides, so 3x = 6 and now we divide both sides by 3 so x = 2.
-Now we have the answer- y=3 and x=2.

Hope this has helped!!

Answer 8

here's an easy way

3x+2y=12.....(1)
3x+y=9 ........(2)

subtract (2) from (1)

2y-y=12-9
>>y=3

substitute back into (2)
3x-3=9
3x =9-3=6
>>x=2

remember,you must do the same thing
to each side of the 'equals' sign-it is
rather like a see-saw-the '=' being the pivot
you can also group two equations
together so long as it suits your purpose
but always remember to treat each side
with equal respect

i hope that this helps

Answer 9

3x+2y=12
3x+y=9

(3x+2y)-(3x+y)=12-9=3 y=3
3x+y=3x+3=9 x=(9-3)/3=2

Answer 10

Take the second equation and multiply it by -2:
-6x-2y=-18

Now add those two equations up:
3x+2y=12
-6x-2y=-18
-3x=-6
x=2

Plug in 2 for x:
3(2)+2y=12
6+2y=12
2y=6
y=3
(2,3)

Check:
3(2)+2(3)=12
6+6=12
12=12

3(2)+3=9
6+3=9
9=9