Question 14, 4.2 .53
HW Score: $57.87 \%, 10$.
Points: 0 of 1
The matrix below is the final matrix form for a system of two linear equations in the variables $x_{1}$ and $x_{2}$. Write the solution of the system.
\[
\left[\begin{array}{rr|r}
1 & -2 & 15 \\
0 & 0 & 0
\end{array}\right]
\]
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The unique solution to the system is $x_{1}=\square$ and $x_{2}=$
B. There are infinitely many solutions. The solution is $\mathrm{x}_{1}=\square$ and $\mathrm{x}_{2}=\mathrm{t}$, for any real number $\mathrm{t}$. (Type an expression using $\mathrm{t}$ as the variable.)
C. There is no solution.
Answer
\(\boxed{\text{Final Answer: There are infinitely many solutions. The solution is } x_{1}=15+2t \text{ and } x_{2}=t, \text{ for any real number } t}\)
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 ：\(\boxed{\text{Final Answer: There are infinitely many solutions. The solution is } x_{1}=15+2t \text{ and } x_{2}=t, \text{ for any real number } t}\)
