# Thread: Help with Simlatineous Equation

1. ## Help with Simlatineous Equation

I know this one should be easy, but i have never been able to get my head round algebra at all.

Simlatanues equation.

3x+4y=18
4x=2+2y

Ive anyone could show me how this is worked out step by step that would be amazing cheers

2. You can solve simultaneous equations either by substitution, or by elimination by addition, or by elimination by subtraction, or by matrix.

If there are only two equations, like your question here, by substitution is enough.
You substitute x for y, or y for x, so that you end up with only y, or only x, or only one variable/unknown.

3x+4y=18 -----Eq.(1)
4x=2+2y ------Eq.(2)

Say we want only x as the unknown. Then we solve for y in terms of x in Eq.(1). Then we substitute that into Eq.(2). Etc...

3x +4y = 18 ----(1)
4y = 18 -3x
y = (18-3x)/4 -----------(1a)
Substitute that into Eq.(2),
4x = 2 +2*(18-3x)/4
Clear the fraction, multiply both sides by 4,
16x = 8 +2(18-3x)
16x = 8 +36 -6x
Isolate the x-terms,
16x +6x = 8 +36
22x = 44
x = 44/22 = 2 ---***
Substitute that into (1a),
y = (18-3x)/4 -----------(1a)
y = (18-3*2)/4
y = 12/4 = 3 -----***

Therefore, x=2 and y=3. ------answer.

Check those on the original equations:

3x+4y=18 -----Eq.(1)
3*2 +4*3 =? 18
6 +12 =? 18
18 =? 18
Yes, so, OK.

4x=2+2y ------Eq.(2)
4*2 =? 2 +2*3
8 =? 2 +6
8 =? 8
Yes, so, OK.

3. Thank you very much for that, i have always struggled with maths.

Thank you for going through that very clearly, was a great help

many thanks

4. Hey there,

sorry but where would i put the lines for these equations on a graphic diagram, i do understand that the lines would cross at point (2,3)

any help please

5. You substitute numbers into the two equations.

Take the first one for example:
3x+4y=18

If x=0
3(0)+4y=18
4y=18
y=18/4
y=9/2

If x=1
3(1)+4y=18
4y=15
y=15/4

And continue with the others.

You plot these co-ordinates onto the graph, and draw the line.

6. ## The graph

Here is the graph: