Step 1 :The given matrix is in row-echelon form. The first row represents the equation \(x_1 - 2x_2 = 15\). The second row, being all zeros, does not provide any additional information.
Step 2 :This means that \(x_2\) can be any real number. We can express \(x_1\) in terms of \(x_2\) (let's call it \(t\)) from the first equation.
Step 3 :So, the solution to the system is \(x_1 = 15 + 2t\) and \(x_2 = t\), for any real number \(t\).
Step 4 :\(t = t\)
Step 5 :\(x1 = 2*t + 15\)
Step 6 :\(x2 = t\)
Step 7 :solution = \((2*t + 15, t)\)
Step 8 :\(\boxed{\text{Final Answer: There are infinitely many solutions. The solution is } x_{1}=15+2t \text{ and } x_{2}=t, \text{ for any real number } t}\)