# Thread: Difficulty on solving a pair of simultaneous equations

1. ## Difficulty on solving a pair of simultaneous equations

Hi all, new here. I've recently began a home study AS/A2 course in mechanical mathematics after being outside of formal education for almost 7 years. I'm currently having problems with remembering methods taught at basic AS level, and in particular the solution and method to this pair of simultaneous equations:

5x + 4y + 5 = 3x - 7y, 4(x+3y) + 3 = 5x

Help would be greatly appreciated!

2. ## Re: Difficulty on solving a pair of simultaneous equations

Originally Posted by FH88
Hi all, new here. I've recently began a home study AS/A2 course in mechanical mathematics after being outside of formal education for almost 7 years. I'm currently having problems with remembering methods taught at basic AS level, and in particular the solution and method to this pair of simultaneous equations:

5x + 4y + 5 = 3x - 7y, 4(x+3y) + 3 = 5x

Help would be greatly appreciated!
I suggest you start by simplfying the equations separately:
5x+ 4y+ 5= 3x- 7y: subtract 3x- 7y+ 5 from both sides
4(x+ 3y)+ 3= 5x: multiply the 4 by both x and 3y then subtract 5x+ 3 from both sides.

3. ## Re: Difficulty on solving a pair of simultaneous equations

Originally Posted by HallsofIvy
I suggest you start by simplfying the equations separately:
5x+ 4y+ 5= 3x- 7y: subtract 3x- 7y+ 5 from both sides
4(x+ 3y)+ 3= 5x: multiply the 4 by both x and 3y then subtract 5x+ 3 from both sides.
Ok, thanks for your reply, so after that and using the elimination method I have:

31x = -27
x = - 31/27

Is this ok?

4. ## Re: Difficulty on solving a pair of simultaneous equations

No. You also need to solve for y.

5. ## Re: Difficulty on solving a pair of simultaneous equations

Ok, I think I've cracked it:

I first simplified the equations to;

2x + 11y = -5,
-x + 12y = -3

Then made the coefficients of y the same value:

24x + 132y = -60,
-11x + 132y = -33

then subtracted leaving with the value of x:

35x = -27,
x = -27/35

substituted back into the first equation, giving me the value of y:

5 -54/35 = -11y
y = -11/35

Is this ok?

6. ## Re: Difficulty on solving a pair of simultaneous equations

You can check yourself...SUBSTITUTE.