What's the Precise Solution?

Algebra Level 3

$| x-1 | + 3y =4$

$x - | y-1 | =2$

What is the precise solution of $x$ and $y$ that satisfy these equations?

Two solution A Unique Solution No Solution None of these

1 solution

Patanjali Dwivedi
Jul 3, 2015

The given equations are

|x-1| + 3y = 4

{x+3y =5 , x>= 1 ......... Eq1 & -x + 3y =3 , x<1 .......Eq2

And

x - |y-1| =2

{ x-y =1 , y>=1 ..........Eq3 & x+ y =3, y<1 .......Eq4

Solving Eq1 & Eq3 , we get x=2 , y=1 A Unique Solution

Solving Eq1 & Eq4 , we get x=2 , y=1 No solution ( since x>=1 & y<1)

Solving Eq2 & Eq3 , we get x=3 , y=2 No solution (since x<1 & y>=1)

Solving Eq2 & Eq4 , we get x=5/2 , y=3/2 No solution (since x<1 , y<1)