Maths-
General
Easy
Question
x2 - 6x + 11 = y
x = y + 1
The system of equations above is graphed in the xy-plane. Which of the following is the y-coordinate of an intersection point (x, y) of the graphs of the two equations?
- -4
- -2
- 2
- 4
The correct answer is: 2
HINT: Substitute one equation in another and then find the y coordinate.
Complete step by step solution:
Let x2 - 6x + 11 = y…(i) and x = y + 1…(ii)
On substituting (ii) in (i), we get (y + 1)2 - 6(y + 1) + 11 = y…(iii)
Using algebraic identity (a + b)2 = a2 + 2ab + b2, expand (iii)
Thus we get, y2 + 2y + 1 - 6y - 6 + 11 = y
On rearranging the above equation, we get y2 - 5y + 6 = 0…(iv)
We can factor the equation as (y - 3) (y - 2) = 0
So y can take the values 2 and 3.
Here only y = 2 matches the option.
Hence option C is the answer.
Note: We can also find the y coordinate of intersection point (x, y) by comparing each option with both the system of equations. Only value that matches both the equations will be 2.
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