1. ## simultaneous equation

hi, im not really sure what to do on this simultaneous equation, here is the question:

i can do simultaneous equations but this one has got me, so any help will be much appreciated!!

thanks!

2. $\displaystyle \boxed{y=3x-11}\;\hdots (1)$

$\displaystyle \boxed{x^2+2xy+3=0}\;\hdots (2)$

substitute (1) in (2)

$\displaystyle x^2+2x(3x-11)+3=0$

$\displaystyle x^2+6x^2-22x+3=0$

$\displaystyle 7x^2-22x+3=0$

solve for x and then find y

3. im not sure how to find x this way, i don't think i have done it like this before.

4. Are you serious?

$\displaystyle \boxed{7x^2-22x+3=0}$ is a quadratic equation!! Follow the same procedure as you did in THIS POST OF YOURS

5. yes i know how to do the quadratic equation but how would have get x and y??

6. Substitution is the only way to solve this because you have different powers of x

You can solve that quadratic to give two values of x:

$\displaystyle 7x^2-22x+3 = (7x-1)(x-3) = 0$

Using those two values of x plug into equation 1 to find their corresponding y values (you will get two pairs of solutions as a final answer)

edit: an example

you know that x = 3 is one of the roots and so you can sub x=3 into eq1 to find y: $\displaystyle y = 3(3) - 11 = -2$

Hence $\displaystyle (3, -2)$ is one pair of solutions. Can you do the same thing for the other root?

which is X and which is Y?

8. so x=3 and y=-6 ??

9. Originally Posted by andyboy179
so x=3 and y=-6 ??

There are 2 solutions for x: your previous post shows you got them: x = 3 or x = 1/7.

Now substitute EACH in the equation y = 3x - 11; you will get 2 corresponding solutions for y ; kapish?

Are you attending math classes?

10. on both of them i got -2 and -10.58??

no, only at school

11. -2 is fine (as worked out in post 6) but $\displaystyle \dfrac{3}{7} - 11 = -\dfrac{74}{7} \approx 10.57$ (the next digit is a 1)

You need to express the roots as pairs though to assign the y values you just found to the x values you used to get them

12. i don't understand "(the next digit is a 1)"
so x=3

13. would this work?
for X i get 3 and 0.14
for Y i get -2 and -10.58

would X=3 and Y=-2 in the end???

14. The next digit is a 1 means I rounded down 10.571 to 10.57

For example you found that when x = 3, y = -2 so a pair is (3,-2)

yes x=3 and y=-2 does work and x = 0.14 and y = -10.57 work

15. so for my answer i could put either one of x=3 and y=-2 and x = 0.14 and y = -10.57.

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