For what values of k is the system of equations 2 k^2 x+3 y-1=0,7 x-2 y+3=0,6 k x+y+1=0 consistent?

Step-by-step solution

We know that three lines a₁ x+b₁ y+c=0, a₂ x+b₂ y+c₂=0 and a₃ x+b₃ y+c₃=0 are concurrerce if aligned & | array lll a₁ & b₁ & c₁ a₂ & b₂ & c₂ a₃ & b₃ & c₃ array |=0 & | array ccc 2 k^2 & 3 & -1 7 & -2 & 3 6 k & 1 & 1 array |=0 & 2 k^2(-2-3)-7(3+1)+6 k(9-2)=0 & 5 k^2-21 k+14=0 & k= 21 161 10 aligned