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With any simultaneous equation the first step has to be get rid of one of the letters...  If you are used to non quadratic simultaneous you have probably been shown a way of doing this where we add the equations together. This example its actually easier than that!

We have been given that y = something involving x  AND y = something else involving x
 So that means the something = the something else

x^2 = 2x - 1

Move all items to one side, because thats how we solve an equation with an x^2

x^2 - 2x + 1 = 0


(x-1)(x-1) = 0

so x = 1. Many Quadratics have more than 1 answer. This is that one case when there is only one answer

y = x^ 2  = 1 ^ 2    so y=1 as well

Hope this helps

This question is basically a part of linear algebra where you need to find the values of the equations. Here, you need to substitute the value of y in the 1st equation as shown below:




factorise the above equation and you find only 1 solution will  be found


so, x=1 and y=1

Hope this help you

So this question is about forming a quadratic equation by subbing the second equation into the first one. If y=x^2 then you can put that into the first one as they are both equation to y. 


x^2 = 2x - 1

if you minus x^2 from both sides you get the equation equal to 0 and then makes what's called a quadratic

0 = -x^2 + 2x - 1

From there it is fairly easy to solve, so quadratics might seem hard to solve but once you get the hang of them they aren't. 

So you are looking for a pair of numbers that multiplies to make 1 and when you add them together they make 2, so the pair of numbers if 1 and 1

That is why both x and y both equal 1 

If y=2x-1 and y = x^2 we can make the equation:

2x-1 = x^2 (rearrange this to get the terms all on one side)

0 = x^2 -2x + 1 (factorise this)

0 = (x-1)(x-1) = (x-1)^2 (this equation only has one solution, x=1)

so if x=1 (y=2x-1, so y =1)

Hopefully this helps


If you draw a y = x^2 curve, you wil see that it is a quadratic a 'U' shape. The y=2x-1 will be a line. Where the two plots cross, you will get your solutions. Picture it graphically, there will be two places, thus two solutions. 

Good evening Han_aa, Do not worry about that at all. I hope you understand my explanation and please do not hesitate to contact me in case of other questions

Hi, you can subtract the second equation from the first, which helps you get rid of y. You get 0=2x-1-x^2 which is equivalent to x^2-2x+1=0. Factorize:           (x-1)(x-1)=0 hence x=1.  When x=1, y=1^2 which is 1. Thus, the solutions are x=1 and y=1. This pair of nubers is the x and the y coordinate of the point of intersection of the straight line and the parabola.

It is very easy, don't worry... 

See, as given, y=2x-1 ....let say this equation no. 1

     and given also, y=x2.......let say this equation no. 2

So from equation no. 2, replace the value of y in equation no. 1, so we get, 


or, x2-2x+1=0

or, x*x -2*x*1 +1 = 0

or, (x-1)(x-1)=0

So, (x-1)=0

or, x=1

So from equation no. 2 we get, y=X2

or, y=x*x

or, y=1*1

or, y=1

So finally we get, both x and y are equal to 1..

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