Question

Solve the system y = 2x – 4 and y = (x – 1)² – 5

Answer 1

`x=2\pm√(3)`

`y=\pm 2√(3)`

Explanation:

Since both equations are equal to y, you can set them equal to each other.

`2x-4=(x-1)^2-5 \\\\\\2x-4=(x^2-2x+1)-4 \\\\\\2x-4=x^2-2x-3 \\\\\\x^2-4x+1=0 \\\\\\x=(4\pm√(16-4))/(2)=(4\pm2√(3))/(2)=2\pm√(3) \\\\\\y=2(2\pm√(3))-4=\pm 2√(3)`

Hope this helps!