Question

3x+2y=12 2x+3y=13 Solve the following equations by Cramer’s rule

Answer 1

Answer:

Check out the attachment for your answer.....

Hope this helps you.....

Answer 2

Given:$\[\frac{3}{x} + 2y = 12,\frac{2}{x} + 3y = 13\]$

To solve the following equation using cramer's rule.

Solution:

Note that from the question, the equations are:

$\[\frac{3}{x} + 2y = 12,\frac{2}{x} + 3y = 13\]$

Assume that, $\[\frac{1}{x} = a\]$

$\[ \Rightarrow 3a + 2y = 12,2a + 3y = 13\]$

Understand that,

$\[\begin{array}{l}\left( {\begin{array}{*{20}{c}}3&2\\2&3\end{array}} \right)\left( {\begin{array}{*{20}{c}}a\\y\end{array}} \right) = \left( {\begin{array}{*{20}{c}}{12}\\{13}\end{array}} \right)\\AX = B\end{array}\]$

Check the value of Δ.

$\[\begin{array}{l}\left| A \right| = \Delta = \left| {\begin{array}{*{20}{c}}3&2\\2&3\end{array}} \right|\\ \Rightarrow \Delta = 9 - 4\\ \Rightarrow \Delta = 5 \ne 0\end{array}\]$

Find $\[{\Delta _a}\] and {\Delta _y}\]$.

$\[\begin{array}{l}{\Delta _a} = \left| {\begin{array}{*{20}{c}}{12}&2\\{13}&3\end{array}} \right|\\ \Rightarrow {\Delta _a} = 36 - 26\\ \Rightarrow {\Delta _a} = 10\end{array}\]$

$\[\begin{array}{l}{\Delta _y} = \left| {\begin{array}{*{20}{c}}3&{12}\\2&{13}\end{array}} \right|\\ \Rightarrow {\Delta _y} = 39 - 24\\ \Rightarrow {\Delta _y} = 15\end{array}\]$

Find the value of a.

$\[\begin{array}{l}a = \frac{{{\Delta _a}}}{\Delta }\\ \Rightarrow a = \frac{{10}}{5}\\ \Rightarrow a = 2\end{array}\]$

Find the value of y.

$\[\begin{array}{l}y = \frac{{{\Delta _y}}}{\Delta }\\ \Rightarrow y = \frac{{15}}{5}\\ \Rightarrow y = 3\end{array}\]$

Find the value of x.

$\[\begin{array}{l}\frac{1}{x} = a\\ \Rightarrow \frac{1}{x} = 2\\ \Rightarrow x = \frac{1}{2}\end{array}\]$

Hence, $\[x = \frac{1}{2},y = 3\]$.