Question

The solution to the system of equations |x + y| = 1 and x - y = 0 is given by which of the following?

• A. $x=y=\frac{1}{2}$
• B. $x=y=-\frac{1}{2}$
• C. $x=1,y=0$
• D. $x=y=\frac{1}{2}$ or $x=y=\frac{-1}{2}$
• E. None of these

Answer 1

The correct option is D $x=y=\frac{1}{2}$ or $x=y=\frac{-1}{2}$

|x + y| = 1, U x + y = 1

or, -(x + y) = 1 i.e., x + y = -1

Solving x + y = 1, x - y = 0, we get

$x=\frac{1}{2}$ and $y=\frac{1}{2}$

Solving x + y = -1 and x - y = 0, we get

$x=-\frac{1}{2}$ and $y=\frac{-1}{2}$

$\therefore x=y=\pm \frac{1}{2}$