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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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