Is 2x - y = 5 and -1/2x + y = 3 perpendicular?

They are not perpendicular.

Hello from MrBillDoesMath!

the lines are not perpendicular (as stated by another writer)

Steps:

Rewrite the first line (2x -y = 5)  as    y =  2x -5.  So it's slope, m1, is "2"

Rewrite the second line ( -1/2x + y =3 ) as  y = +1/2x + 3. So it's slope, m2, is +1/2.

Two lines are perpendicular if m1 * m2 = -1 which is NOT the case here (For us, m1 * m2  = 2 * (+1/2) =  + 1 which is not -1. As they say, "close, but no cigar!)

Regards,  MrB

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11