Question

solve by cramers rule
3x – 2y = 4
-6x + 4y = 7

Answer 1

Solve the following equations by Cramer's Rule

• 3x - 2y = 4

• - 6x + 4y = 7

The matrix form of the above equation is

$\rm :\longmapsto\:\: \begin{bmatrix} 3 & - 2\\ - 6 & 4\end{bmatrix}\begin{gathered}\rm \left[\begin{array}{c}x\\y\end{array}\right]\end{gathered} = \begin{gathered}\rm \left[\begin{array}{c}4\\7\end{array}\right]\end{gathered}$

Here,

$\rm :\longmapsto\:A\: = \begin{bmatrix} 3 & - 2\\ - 6 & 4\end{bmatrix}, \: X = \begin{gathered}\rm \left[\begin{array}{c}x\\y\end{array}\right]\end{gathered}, B = \: \begin{gathered}\rm \left[\begin{array}{c}4\\7\end{array}\right]\end{gathered}$

Now,

Consider,

$\rm :\longmapsto\:D \: = |A| \: = \begin{array}{|cc|}\sf 3 &\sf - 2 \\ \sf - 6 &\sf 4 \\\end{array} = 12 - 12 = 0$

it implies, that system of equations is either consistent or inconsistent.

Now,

Consider,

$\rm :\longmapsto\:D_1 \: = \begin{array}{|cc|}\sf 4 &\sf - 2 \\ \sf - 7 &\sf 4 \\\end{array} = 16 - 14 = 2 \ne \: 0$

Since,

$\rm :\longmapsto\: |A| = 0 \: \: and \: \: D_1 \ne \: 0$

$\bf\implies \:System \: of \: equations \: has \: no \: solution$