Question

Solve the following equation by using Cramer's rule 8x-4y= 2, x + 2y = 4

Answer 1

Answer:

The value of $x=2,\ y=\frac{3}{2}$

Step-by-step explanation:

For the equations

$8x-4y=2\\\\x+2y=4$, the coefficient matrix is

$D=\left[\begin{array}{ccc}8&-4\\1&2\\\end{array}\right]$, variable matrix $X=\left[\begin{array}{ccc}x\\y\\\end{array}\right]$ and solution matrix $B=\left[\begin{array}{ccc}2\\4\end{array}\right]$.

$det D=8(2)+4=20$

$D_{1}$ is the matrix obtained by replacing the first column of $D$ by $B$.

$D_{1} = \left[\begin{array}{ccc}2&-4\\4&2\\\end{array}\right]$, $det D_{1}=4+16=20$

$D_{2} =\left[\begin{array}{ccc}8&2\\1&4\\\end{array}\right]$, $det D_{2} =32-2=30$

By creamer's rule,

$x=\frac{det D_{1} }{det D}$,    $y=\frac{det D_{2}}{det D}$

therefore, $x=1,\ y=\frac{3}{2}$.

hence the answer.

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