Question

What is the Cramer’s method?

Answer

$A_{1}x+B_{1}y=C_1 \dots (1)$
$A_{2}x+B_{2}y=C_2 \dots (2)$
$\text{By indicating as}$
$∆=\left|\begin{array}{cc}{A}_1& B_1\\ A_2& B_2\end{array}\right|=A_1{B}_2–A_2{B}_1$
$\mathrm{Where\; ∆\; is\; the\; determinant\; of\; the\; system.}$
$∆x=\left|\begin{array}{cc}{C}_1& B_1\\ C_2& B_2\end{array}\right|=C_1{B}_2–B_1{C}_2$
$∆y=\left|\begin{array}{cc}{A}_1& C_1\\ A_2& C_2\end{array}\right|=A_1{C}_2–A_2{C}_1$
$x=\frac{∆x}{∆},y=\frac{∆y}{∆}$

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