Question

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

Answer 1

Answer:

$x=2\pm\sqrt{3}$

$y=\pm 2\sqrt{3}$

Step-by-step explanation:

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

$2x-4=(x-1)^2-5 \\\\\\2x-4=(x^2-2x+1)-4 \\\\\\2x-4=x^2-2x-3 \\\\\\x^2-4x+1=0 \\\\\\x=\dfrac{4\pm\sqrt{16-4}}{2}=\dfrac{4\pm2\sqrt{3}}{2}=2\pm\sqrt{3} \\\\\\y=2(2\pm\sqrt{3})-4=\pm 2\sqrt{3}$

Hope this helps!