Question

3. Which coordinate pair is a solution to the following system?

(6)
A)
(6,4)
B) (-4,-6)
y=x²-4x+6
-x + y = 2
C) (3, 1)
D) (1,3)

Answer 1

Answer: D) (1,3)

Explanation:

`\displaystyle\\\left \{ {{y=x^2-4x+6} \atop {-x+y=2}} \right. \ \ \ \ \left \{ {{y=x^2-4x+6} \atop {-x+y+x=2+x}} \right. \ \ \ \ \left \{ {{y=x^2-4x+6\ \ \ \ (1)} \atop {y=2+x\ \ \ \ \ (2)}} \right. \\`

Equate equations (1) and (2):

`x^2-4x+6=2+x\\`

We transfer the left side of the equation with the opposite sign to the right side of the equation:

`x^2-4x+6-2-x=0\\(x^2-x)-(4x+4)=0\\x*(x-1)-4*(x-1)=0\\(x-1)*(x-4)=0\\x-1=0\\x_1=1\\y=2+1\\y_1=3\\Hence,\ (1,3)\\x-4=0\\x_2=4\\y=2+4\\y_2=6\\Hence,\ (4,6)`