Describe the set of solutions x x1 x2 x3 element of real num

Describe the set of solutions x =(x_1, x_2, x_3) element of real numbers^3 of the system of equations x_1-x_2+x_3=0 x_1+2x_2+x_3=0 2x_1+x_2+2x_3=0}.

Solution

given equations are x1-x2+x3=0 -->equation1

x1+2x2+x3=0-->equation2

2x1+x2+2x3=0-->equation3

subtract equation1 -equation2

-3x2=0

so x2=0

the equations become

x1+x3=0

x1+x3=0

so x1=x and x3=-x

(x,0,-x)

2x1+2x3=0