Simultaneous Equation help (1 Viewer)

[cUfffsxd]

srry if in wrong section!

More to the point. My class kinda skipped Simultaneous Equations today claiming it was to hard ><" but i like it (only in 10-general) but i have been doing it for last 30-1hour and came into some trouble;

3x-2y = 9
x+2y = 7

can anyone explain how to do this please?
I dont get if "3x = 9+2y", if to do that or divide by 3 seems its 3x or start with
"2y = 7-x" which i tried and got wrong >:

 

[occer]

4x = 16
x = 4.

It's basic sim. eqns. all you need to do is either add both the top and the bottom similar terms or subtract them.

 

[ascentyx]

Okay there is 2 basic ways you learn to do these in yr10.

First one is the elimination method.

3x-2y = 9
x+2y = 7

If you notice that (-2y) + (2y) = 0, you can simply add the first and second equation eliminating the y variable and leaving (3x+x) = (9+7) ie x = 4.

Then you simply sub 4 into any of the above equations and it will give you a value for y, that is your solution.

Alternatively you can use substitution (inefficient in this case but i'll still explain it)

You could rearrange the bottom equation to x = 7-2y.

Then you could sub this into the first one getting 3(7-2y) - 2y = 9

ie y= 3/2.

Another way which is awesome but pointless in year 10 is making a matrix and reducing it through elementary row operations to echelon form.

 

[Zantico]

SUBSTITUTION METHOD! FOR YOU
3x-2y = 9 (1)
x+2y = 7 (2)

x= 7-2y (2A)

Substitute (2A) into (1)

3(7-2y)-2y=9

21-6y-2y=9
-8y +21=9
8y= 12
y=12/8
y=3/2
substitue y=3/2 into (2)

x=7-2(3/2)
x=4

 

[cUfffsxd]

ahh thx yes i am using substitution method.

thx for help :>!

 

[maths94]

3x-2y = 9...[1]
x+2y = 7....[2]

[1] + [2]

4x=16

x=4

substitue x=4 into equation [1]

3(4)-2y=9

12-2y=9

-2y=-3

y=3/2

subtitute x=4 and y=3/2 into equation....[2]

4+2(3/2)=7

4+3=7

7=7<--shows it works

substitue x=4 and y=3/2 into equation...[1]

3(4)-2(3/2)=9

12-3=9

9=9<---shows that it works

So we showed what x and y was....x=4, y=3/2...we substitued those values into each equation and found out they fit/work. so thats your answer.

 

[Timothy.Siu]

thats a bad way to show it...

anyone can say 9=9

7=7
that doesn't mean anything.

 

[ninetypercent]

i think you will get marked down if you show it by saying 9=9. In some problems, you need to take the LHS and RHS to show that it works:

In equation One,
LHS = 3(4)-2(3/2)
= 9
= RHS

therefore, x = 2 and y = 3/2 are solutions to equation one

In equation two,
LHS = 12-2(3/2)
= 7
= RHS

therefore x = 4 and y = 3/2 are solutions to the equations

Overall solutions: x = 4, y = 3/2

 

[Aquawhite]

[1] + [2]

4x=16

x=4

substitue x=4 into equation [1]

3(4)-2y=9

12-2y=9

-2y=-3

y=3/2

subtitute x=4 and y=3/2 into equation....[2]

4+2(3/2)=7

4+3=7

7=7<--shows it works

substitue x=4 and y=3/2 into equation...[1]

3(4)-2(3/2)=9

12-3=9

9=9<---shows that it works

So we showed what x and y was....x=4, y=3/2...we substitued those values into each equation and found out they fit/work. so thats your answer.

Farrout! How'd you do that?! I can't believe that 9=9...

My logic and world has been turned upside down.

 

[maths94]

Farrout! How'd you do that?! I can't believe that 9=9...

My logic and world has been turned upside down.

how u rkn i got x and y values fromm.. i guessed that?...

 

[maths94]

thats a bad way to show it...

anyone can say 9=9

7=7
that doesn't mean anything.

yes thats true but i found the correct x and y values and i am just putting them into the equation to see if the fit/work.

 

[boo92]

you shouldnt need to put in the 9=9 and so forth. all you need to do is find the solutions i.e. x=..., y=... the substitution at the end (the 9=9 bit) is only necessary for your own head. it just ensures you have gotten it right. NOT NECESSARY!! but good if you are not sure if it is right or if you have extra time in an exam.

 

[Amogh]

you shouldnt need to put in the 9=9 and so forth. all you need to do is find the solutions i.e. x=..., y=... the substitution at the end (the 9=9 bit) is only necessary for your own head. it just ensures you have gotten it right. NOT NECESSARY!! but good if you are not sure if it is right or if you have extra time in an exam.

exactly
you dont necessarily prove through the LHS and RHS method that the x and y values are correct.
It is solely for your reassurance. Just do it in your head.