Chapter ISG, Problem 9.7.9P

To determine

To find solution of system of equation algebraically.

Answer to Problem 9.7.9P

Then points of intersection are $(3,3)$ and $(3,3)$

Explanation of Solution

Given information:

  $y=x^2-4x+6$

  $y=2x-3$

Calculation:

  $y=x^2-4x+\mathrm{6..........}(1)$

  $y=2x-\mathrm{3.............}(2)$

put value of y from equation(2) in (1)

  $2x-3=x^2-4x+6$

On solving,

  $0=x^2-4x+6-2x+3$

On solving,

  $0=x^2-6x+9$

On solving,

  $x^2-6x+9=0$

On solving,

  $x^2-3x-3x+9=0$

On solving,

  $x(x-3)-3(x-3)=0$

On solving,

  $(x-3)(x-3)=0$

On solving,

  $(x-3)=0$

  $(x-3)=0$

On solving,

  $x=3$

  $x=3$

If $x=3$

  $y=2(3)-3$

On solving,

  $y=3$

If $x=3$

  $y=2(3)-3$

On solving,

  $y=3$

Then points of intersection are $(3,3)$ and $(3,3)$