If the system of linear equations x - 2y + 5z = 3 2x - y + z = 1 11x - 7y + z = has infinitely many solutions, then the value of + is equal to :

Step-by-step solution

For a system of linear equations to have infinitely many solutions, we must have = 0 and _x = _y = _z = 0 . First, set = 0 : = vmatrix 1 & -2 & 5 2 & -1 & 1 11 & -7 & vmatrix = 0 1(- + 7) - (-2)(2 - 11) + 5(-14 + 11) = 0 - + 7 + 4 - 22 + 5(-3) = 0 3 - 15 - 15 = 0 3 = 30 = 10 Next, set _z = 0 : _z = vmatrix 1 & -2 & 3 2 & -1 & 1 11 & -7 & vmatrix = 0 1(- + 7) - (-2)(2 - 11) + 3(-14 + 11) = 0 - + 7 + 4 - 22 + 3(-3) = 0 3 - 15 - 9 = 0 3 = 24 = 8 Therefore, the value of + = 10 + 8 = 18 . Answer: 18