# At what point does the curve y = 3x^2 - 5x + 3 meet the line y= x.

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### 2 Answers

At the point where the curve y = 3x^2 - 5x +3 meets the line y = x, the x and y coordinates are the same.

So we have y = 3x^2 - 5x +3 = x

=> 3x^2 - 6x + 3 = 0

=> x^2 - 2x + 1 = 0

=> (x - 1)^2 = 0

=> x - 1 = 0

=> x = 1

y = x = 1

**The point of intersection is (1 , 1)**

Given the curve 3x^2 5x + 3 and the line y= x

We need to find the intersection points between the curve and the line y.

The points of intersections are the points that verifies the following.

==> 3x^2 - 5x + 3 = x

Let us move x to the left side.

==> 3x^2 - 6x + 3 = 0

Now we will divide by 3.

==> x^2 - 2x + 1 = 0

Now we will factor.

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

==> x = 1

==> y= 1

**Then the point of intersection is (1,1)**