Exercise · ZW-CRAMERS-RULE-003 · ★★☆ Intermediate
Solve for \(y\) with Cramer's rule: \(\begin{cases}x+2y=8\\ 3x-y=3\end{cases}\).
Choose one option.
Show answer
- B. \(y=3\)
Explanation
\(\det A=-1-6=-7\) and \(y=\dfrac{\det\begin{pmatrix}1&8\\3&3\end{pmatrix}}{-7}=\dfrac{3-24}{-7}=3\). Forgetting the sign of \(\det A\) gives \(-3\).
Review the concept: Cramer's rule
Cramer's rule gives the unique solution of a square system, whose coefficient matrix \(A\) has nonzero determinant, as a quotient of determinants.
\[x_i=\frac{\det A_i}{\det A}\]
More practice problems: cramer's rule
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