How do I work out this simultaneous equation?

Question

3x - 2y = 9
2x - y = 5

This is part of gcse revision, so any help would be greatly appreciated, thanks.

Answer 1

Elimination by addition Method

3x - 2y = 9- - - - - -Equation 1
2x - y = 5- - - - - - -Equation 2
- - - - - - -

Multiply equatin 2 by - 2

2x - y = 5

- 2(2x) - (- 2)(y) = - 2(5)

- 4x - (- 2y) = - 10

- 4x + 2y = - 10

-- - - - - - - - -

3x - 2y = 9
- 4x + 2y = - 10
- - - - - - - - - -
-x = - 1

- 1(- x = -1(- 1)

x = 1

Insert the x value into equation 1

- - - - - - - - - - - - - - - - - - - - - - - - -

3x - 2y = 9

3(1) - 2y = 9

3 - 2y = 9

3 - 2y - 3 = 9 - 3

- 2y = 6

- 2y - 2 = 6/ - 2

y = - 6/2

y = - 3

Insert the y value into equation 1

- - - - - - - - - - - - -- - - - - - - - - - - -

Check for equation 1

3x - 2y = 9

3(1) - 2(- 3) = 9

3 - (- 6) = 9

3 + 6 = 0

9 = 9

- - - - - - - - -

Check for equation 2

2x - y = 5

2(1) - (- 3) = 5

2 + 3 = 5

5 = 5

- - - - - - - - - -

Both equations balance

The solution set { 1, - 3 }

- - - - - - - - -s-

Answer 2

there are a lot of method of solution for this particular equations

you can use elimination by subtraction and addition by setting the coefficients of one variable to the same value

like multiplying the second equation by - 2 then add to the first equation

3x - 2y = 9
-4x + 2y = -10

the result if we add is

-x = -1 or x = 1 then substitute the value of x to any of the equation to get the value of y

y = - 3

another method is by elimination by substitution

sample express the y from the second expression in terms of x

y = 2x - 5

then substitute this to the first equation

3x - 2(2x -5) = 9 on the second term distribute 2

3x - 4x + 10 = 9 then

-x = 9 - 10 = -1

x = 1 then substitute the value of x to any of the given equation to solve the value of y

y = - 3

another method is by determinants but i can't show you here.

Answer 3

3x - 2y = 9
2x - y = 5

multiply the whole second equation by -2:
3x - 2y = 9
-4x + 2y = -10

Add the two equations and get:
-1x = -1

Divide by -1 and get x = 1

Now sub in 1 for x in either of the original equations and get that y = -3

So x = 1, y = -3

Answer 4

Pretty simple.
But first, I have to explain some properties of equations.
If you multiply all the equation by a number, and that is both sides, the value of the variable that solves the equation still is the same.
So, a=b is the same as ac=bc.

Also, you can sum equations, because basically each side is the same thing, and a=b is the same as a+c=b+c.
So with this, we can make:

3x - 2y = 9
2x - y = 5

I multiply the second equation by -2.
3x - 2y=9
-4x + 2y = - 10

Notice the number I used to multiply the one of the equations, I was trying to get inverse additives with the y! If you try this with the x you should be able to solve it too.

I sum them both and get a linear equation with one variable.
-x = -1
So, X = 1

I solve one of the original equations with x=1
2-y=5
-y=3
y=-3

Hope this long explanation works. :P

Answer 5

OK, the 1st step is to think of how u can get rid of one unknown, that is either x or y. I suggest u go for getting rid of y. This is how it's done,
3x - 2y = 9
(2x-y=5 ) X2 (u have to multiply the whole equation by 2 and u get,) 4x-2y=10. now u subtract the 1st equation from this new equation u derived.
4x-2y-(3x-2y) = 10-9
4x-2y-3x+2y=1
X=1, now u substitute this in one of the 2 equations,
3(1)-2y=9
-2y=9-3
y=-3. hope this helps

Answer 6

3x-2y=9
2x-y=5

3x - 2y = 9
x by -2 -4x+2y =-10

x=1
y=-3

Answer 7

3x-2y=9 equation 1
2x-y=5 equation2 x -2
3x-2y=9
-4x+2y= -10
-x= -1divide both side by -1
x=1
subtitute for x=1 in equation 1
3x-2y=9
3(1)-2y=9
3-2y=9
-2y=9-3
-2y=6
-2y/-2=6/-2
y= -3
x=1,y= -3

Answer 8

3x - 2y = 9
2x - y = 5

-4x + 2y = -10
3x - 2y = 9

-x = -1

x = 1
y = -3

Answer 9

y=2x-5
3x-2(2x-5)=9
3x-4x+10=9
-x+10=9
-x=-1
x=1

2(1)-y=5
2-y=5
-y=3
y=-3

so, x= 1 and y= -3
basically you solve for one letter, then substitute it in for the other letter...this is called the substitution method

Answer 10

Another way to work it out would be to plot the two as lines -Descartes style and see where the point of intersection is!!