[quote]jtg987 wrote:

Hi everyone havent done maths since highschool(in third year uni) and am quite stuck on this one problem, I’m probably doing just one thing wrong but cant figure it out

Solve the following linear simultaneous equation systems for y and x.

(a) y = 8x + 4 ; 3y=2x-6

it would be appreciated if someone could lend a hand

cheers[/quote]

edit: I don’t know how to make it nice and neat so i just gave everything it’s own line for the sake of it.

This is the simplest way to solve it:

y = 8x +4 -A

3y = 2x -6 -B

multiply A by 3 and subtract B from A.

3y = 24x + 12

0y = 22x + 18 (its 12 MINUS MINUS 6 which is the same as 12 + 6 )

So now 0 = 22x +18

-18 = 22x

-18/22 = x

You can simplify by dividing both 18 and 22 by 2

which gives

-9/11 = x

Then to get y you just plug back in your value of x.

You can pick either y formula given but i’ll do both for the sake of completion.

A: y = 8x +4 =>

y = 8(-9/11) + 4

= -72/11 + 4

= -72/11 + 4 * 1

= -72/11 + 4 * (11/11 = 1)

= -72/11 + 44/11

```
y = -28/11
```

B: 3y = 2x -6 =>

3y = 2(-9/11) -6

= (-18/11) - (6 times 1 = 6)

= (-18/11) - (6 times 11/11 = 6)

= (-18/11) - 66/11 = -84/11

```
3y = -84/11
y = (-84/11)/3
```

= (-84/1) times (1/11) times (1/3) — (you can rearrange it however you like it doesn’t matter)

= (-84/3)/11

= -28/11

So,

x is -9/11

y is -28/11

If you don’t get anything write it out on paper. Doing the problem/solution yourself is usually more helpful in making you understand it than doing mental mathematics, even if you’re just copying it. As long as you try to understand it as you rewrite it, you’ll get it.