For what value of k does the system of linear equations `2x+3y=7` `(k-1)x + (k+2)y =3k` have an infinite number of solutions

Explanation

`2x + 3y- 7 =0 and (k - 1 ) x + ( k + 2) y - 3k =0 `.
For infinitely many solutions, we have ` (a_1)/(a_2) = (b_1)/(b_2) = (c_1)/(c_2)`.
` therefore (2)/(( k - 1 )) = (3)/((k + 2 )) and (3)/((k + 2))= ( 7)/(3k )`
` rArr 2k + 4 = 3 k - 3 and 9k = 7k + 14 rArr k = 7`.