Can Cramer's rule be used to solve this system of equations?
\[
\left\{\begin{array}{ll}
x_{1} & =-2 \\
-3 x_{1}+x_{2} & =3
\end{array}\right.
\]
Yes
No
If Yes, write the determinants used to compute $x_{2}$.
Compute
\[
x_{2}=
\]
Answer
The solution to the system of equations is \(x_{1} = -2\) and \(x_{2} = -3\). Cramer's rule was not needed to solve this system of equations. Therefore, the answer to the question 'Can Cramer's rule be used to solve this system of equations?' is \(\boxed{\text{No}}\).
Step 1 ：Cramer's rule is a method used to solve systems of linear equations by expressing the solutions in terms of determinants. However, in this case, the system of equations is not in the standard form for applying Cramer's rule. The first equation is simply \(x_{1} = -2\), which doesn't involve \(x_{2}\). The second equation can be rewritten as \(-3x_{1} + x_{2} = 3\), but we already know the value of \(x_{1}\) from the first equation. Therefore, we can substitute \(x_{1} = -2\) into the second equation to solve for \(x_{2}\). There's no need to use Cramer's rule in this case.
Step 2 ：The solution to the system of equations is \(x_{1} = -2\) and \(x_{2} = -3\). Cramer's rule was not needed to solve this system of equations. Therefore, the answer to the question 'Can Cramer's rule be used to solve this system of equations?' is \(\boxed{\text{No}}\).
