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Solve the simultaneous equations 5x + 3y = 24 and 3x - 4y = 26

Ok, so here are the equations

5x+3y=24

3x-4y=26

So let's multiply the first equation by 3, which gives us:

15x+9y=72

Now let's multiply the second equation by 5, which gives us:

15x-20y=130

So we're now left with:

15x+9y=72

15x-20y=130

Let's rearrange both of these equations to make 15x the subject. So now we're left with:

15x = 72-9y

15x= 130+20y

Now we can compare these two equations, to give us:

72-9y=130+20y (=15x)

If we rearrange this new equation, we find that:

20y + 9y = 72 - 130

29y = -58

y = -2

Since we now have a value for y, we can substitute this back into 5x + 3y = 24

5x + 3(-2) = 24

5x -6 = 24

5x = 30

x = 6

So, are final answer is x = 6 and y = -2

William S. 11 Plus Maths tutor, A Level Maths tutor, 13 plus  Maths t...

1 year ago

Answered by William, a GCSE Maths tutor with MyTutor


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