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Stuck on Simultaneous Equations

Can anybody show me how to do the following questions please im having a hard time getting the right answer.

3x+4y = 10
7x - 5y = 9

x+y =2
3x²-2x + y² = 2

Thanks in advance

Reply 1

Jodin

The usual idea is to eliminate one variable by writing it in terms of other variables, so for example
3x+4y = 10
7x - 5y = 9

If you now say that y = (10-3x)/4 now whenever you see a y you can replace it with this equation that has x in it, so if we put it into our second bit we get 7x + (-50+15x)/4 = 9
which means 28x +15x = 36 + 50, 43x = 86, x = 2 and so y = (10-6)/4 = 1.

You can then check this by putting it back into your equations 3*2+4 = 10 and 7*2 - 5 = 9, it's all good. Same idea with the 2nd question but now to obtain x/y you'll need to solve a quadratic after your substitution.