-5 x-10,4=0 -2 x^2+(x)/(2)=0

To solve the given system of equations, we can use the substitution method. Let's solve for x in the first equation:<br /><br />\(-5x - 10.4 = 0\)<br /><br />Adding 10.4 to both sides, we get:<br /><br />\(-5x = 10.4\)<br /><br />Dividing both sides by -5, we find:<br /><br />\(x = -2.08\)<br /><br />Now, substitute this value of x into the second equation:<br /><br />\(-2x^2 + \frac{x}{2} = 0\)<br /><br />Substituting \(x = -2.08\), we get:<br /><br />\(-2(-2.08)^2 + \frac{-2.08}{2} = 0\)<br /><br />Simplifying the equation, we find:<br /><br />\(2(4.3364) - 1.04 = 0\)<br /><br />\(8.6728 - 1.04 = 0\)<br /><br />\(7.6328 = 0\)<br /><br />Since the left-hand side of the equation is not equal to zero, there is no solution for the second equation. Therefore, the correct answer is \(x \in \emptyset\), which means that there is no solution for x in the given system of equations.