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# Simultaneous Equations Help! watch

1. Hi,

I have tried to do questions 7 & 9 but I am really stuck on them since I am getting them wrong.
x=2/3, y=1/3. Or x=1/3, y=2/3
(6, -6); tangent
I have attached the questions and my workings

Thanks!
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2. (Original post by musicangel)
Hi,

I have tried to do questions 7 & 9 but I am really stuck on them since I am getting them wrong.
x=2/3, y=1/3. Or x=1/3, y=2/3
(6, -6); tangent
I have attached the questions and my workings

Thanks!
For Q7 write y in terms of x using the linear equation. Yoy should get y= 3x/4 -13
Then put that back into the equation of the circle. So where you see a y term in the circle equation - replace it with 3x/4 -13
Then expand the brackets and use the quadratic formula to solve for x. Then find the corresponding y values for each x value found. Do the same with the next question. Write y in terms of x in the linear equation - by just dividing everything by 4. Then substitute that y value (in terms of x) into the equation of the circle. Then expand the brackets and form a quadratic equation =0
Then use the quadratic formula to solve for x. Then find the corresponding y value. You should notice that there is only value for the point of intersection. This means that the line is tangent to the circle - by definition a tangent will only intersect a circle at one point
3. (Original post by musicangel)
Hi,

I have tried to do questions 7 & 9 but I am really stuck on them since I am getting them wrong.
x=2/3, y=1/3. Or x=1/3, y=2/3
(6, -6); tangent
I have attached the questions and my workings

Thanks!
For question 7, try to write the other equation in terms of x and y first so like x^2 +something xy + y^2. You can multiply through by 2 to get rid of the fractions. Then substitute in your value for y (y=1-x). It comes out as a quadratic which you can then solve using the quadratic formula. Hopefully that makes sense. I have done the question using this method and I got the answers you gave there Also, don't forget to substitute your x-values back into the equation to get the y-values

I'm still trying question 9 on my own first, but will let you know once I have figured out a method

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