Geometry With Triangles With 3 Variables

Question

The angles of a triangle are $x$,$y$ and $z$ in descending order.If $2x-y=100^\circ =3y-2z$ ,then its smallest angle is?

My answer is coming $40^\circ$ but the book is showing answer $60^\circ$ Is the answer really $60^\circ$ ?

Answer 1

Hint:

We have the following relations: $$x+y+z = 180^\circ \tag 1$$ $$ x = \frac{y + 100^\circ}{2} \tag 2$$ $$z = \frac{3y -100^\circ}{2} \tag 3$$

Can you find $x,y,z$ from $(1)\, , (2)\, , (3)?$

Answer 2

we get three equations $$2x-y=100^{\circ}$$ $$3y-2z=100^{\circ}$$ $$x+y+z=180^{\circ}$$ can you solve this System? solving this System we get $$80^{\circ},60^{\circ},40^{\circ}$$