How do you solve the following simultaneous equations with the algebraic method rather the than the graphical:
2x + 5y = 4
3x + 4y = 13

Thankyou very much for your help I have my gcse maths paper 1 on monday and I'm stuck on this wjec past paper:(

You can do it any number of ways.  One is by elimination of one variable.

Do this by multiplying the top equation by 3, the bottom by 2, and subtracting them:

  6x + 15y = 12
- (6x + 8y = 26)
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 0x + 7y = -14

y = -2

Plug into either equation and you get x = 7

The other usual method is substitution.  You re-arrange one equation to e.g. get y in terms of x, substitute that for y in the other equation, and solve for x.  Example:

2x + 5y = 4
5y = 4 - 2x
y = (4-2x)/5

3x + 4(4-2x)/5 = 13     Now solve for x.