Answer:
Step-by-step explanation:
To solve the system of equations y = (x-1)² and y-x=1, we can substitute the expression for y in the second equation with the expression for y in the first equation. This gives us:
(x−1)2−x=1
Expanding the square, we get:
x2−2x+1−x=1
Simplifying the equation, we get:
x2−3x=0
Factoring out x, we get:
x(x−3)=0
Therefore, the solutions to the system of equations are:
x=0
x=3
To find the corresponding values of y, we can substitute each value of x into the equation y = (x-1)². This gives us:
(x,y)=(0,1)
(x,y)=(3,4)
Therefore, the solutions to the system of equations y = (x-1)² and y-x=1 are:
(x,y)=(0,1)
(x,y)=(3,4)
