I need help with my maths homework, simultaneous equations.?

Question

Hi, i am stuck on my maths homework, we are studying simultaneous equations, and my question is;

3x+2y=7

2x+3y=9

I need to work out what x and y both, individually equal,

please can somebody help, also, I want working out, as I don't want to just copy,

10 points to first person who helps me, correctly.

Answer 1

You want to "kick out" one of your two variables to find out the other one. When you know one of the two, you can easily find the second.

For example, you eliminate the x, by multipliing the second equation with 3/2.

You now have  3x+2y=7       (1)

                     3x+9/2*y=27/2   (2)

Now you calculate equation(1)-equation (2 ) , you have 5/2*y=13/2 , as 3x-3x=0 and 9/2*y - 2y= 9/2*y - 4/2*y=5/2*y

you finally multiply your equation with 2/5 so that just y remains on the left side: y= (13/2)*(2/5) = 26/10=2.6

Now you insert this value for y and calculate x: 3x+2*2.6=7 | -(2*2.6)

                                                                    3x=7-(2*2.6) | /3

                                                                    x= [7-(2*2.6)]/3

                                                                      =(7-5.2)/3

                                                                      =0,6

Finally, x= 0,6 and y= 2,6.  

Answer 2

multiply the 1st equation by 2 and the 2nd by 3 to get:

6x+4y=14

6x+9y=27

Subtract the 1st from the 2nd to get

0x +5y=13

therefore y=13/5 ... doesn't sound right for simple examples of simultaneous equations!!

... are you sure you've got the signs correct?

I suspect the 2nd equation should be 2x-3y=9 !!

in which case the equations become (after multiplication)

6x+4y=14

6x-9y=27

subtracting 1st from 2nd gives:

-13y=13 so y=-1

then substituting this back into equation 1 gives 3x=9 so x=3

Answer 3

There are multiple ways of approaching this problem.  

1)  Solve the first equation for X in terms of Y

( 3x + 2y = 7 -> x = (7-2y)/3).  

Use this in place of X in the second equation:

2*(7-2y)/3 + 3y = 9.

Solve for Y.  (you can similarly start by solving for Y, plugging in, and solving for X - it really doesn't matter)

2) Multiply the entire first equation by a constant that will allow you to add the two equations together and eliminate a term:

3x + 2y = 7 -> -2x + (-2/3)*2y = (-2/3)*7

-2x - 4/3y = -14/3

2x + 3y = 9

_________________

3y-4/3y = 9-14/3

Solve for y, plug back into either equation and solve for X.

3) There are various other ways of solving this type of question (especially if you have access to a graphing calculator of decent power: TI-89, etc), but those are the first two you learn.

Answer 4

x=(7-2y)/3 and from the 2nd eq.x=(9-3y)/2,x==x then,14-4y=27-9y

then 5y=13,y=13/5,then 3x+26/5=7=35/5,3x=9/5,x=3/5

======================================...

CHECK:     3(3/5)+26/5=35/5=7 & 6/5+39/5=45/5=9

                    GOOD LUCK on your studies.

Answer 5

well you need to eliminate one of the coefficients - either X or Y

so you need to do something to both the equations so that either the X or the Y values are equal

so

3x+2y=7...equation 1

2x+3y=9...equation 2

multiply e1 by 2, and e2 by 3.

this gives u

6x+4y = 14....e1'

6x+9y=27...e2'

so take e2' away from e1'

6x+4y=14 -  6x+9y=27

that gives you

-5y= -13

so basically 5y=13

y=5/13

then once you know the value of Y you can substitute that in to one of the equations to get X.

hope that helped :)

Answer 6

- 6x - 4y = - 14

6x + 9y = 27------ADD

5y = 13

y = 13/5

3x + 26/5 = 7

3x = 9/5

x = 3/5

x = 3/5 , y = 13/5

Answer 7

Well, the easiest way to do this is to pick one of the two variables (x or y) and multiply either or both equations by a constant in order to make the coefficient equal in both equations. For example:

3x + 2y = 7

2x + 3y = 9

Multiply the first by 3 and the second by 2:

9x + 6y = 21

4x + 6y = 18

Now, subtract the second from the first, and you're left with:

5x = 3

x = 3/5

Now, substitute 3/5 for x in either of the first two equations:

3(3/5) + 2y = 7

Multiply the whole thing by 5 to get rid of the fraction:

9 + 10y = 35

Subtract 9:

10y = 26

Divide by 10

y = 26/10 = 13/5

So, x = 3/5 and y = 13/5

To verify your answers, substitute these values back into the other equation:

2(3/5) + 3(13/5) = 9

6/5 + 39/5 = 9

45/5 = 9

9 = 9

QED

Answer 8

You have to find x or y and than substitute for ex in the first one

X= ((7-2y)/3)

then u can substitute x in the equations