Question

solve for x and y by suitable method 2x + Y + 5 is equal to zero 3 x minus 2 Y - 12 is equal to zero​

Answer 1

Solving by matrices...

We have the equations,

$2x+y=-5\\\\3x-2y=12$

So we have the matrix,

$\left [\begin {array}{cc|c}2&1&-5\\3&-2&12\end {array}\right]$

Let's begin!

$\left [\begin {array}{cc|c}2&1&-5\\3&-2&12\end {array}\right]\xrightarrow{R_2-R_1\to R_1}\left [\begin {array}{cc|c}1&-3&17\\3&-2&12\end {array}\right]\\\\\\\xrightarrow{3R_1-R_2\to R_2}\left [\begin {array}{cc|c}1&-3&17\\0&-7&39\end {array}\right]\xrightarrow{-\frac {1}{7}R_2\to R_2}\\\\\\\left [\begin {array}{cc|c}1&-3&17\\0&1&-5\frac {4}{7}\end {array}\right]\xrightarrow{R_1+3R_2\to R_1}\left [\begin {array}{cc|c}1&0&\frac {2}{7}\\0&1&-5\frac {4}{7}\end {array}\right]$

So, finally,

$\largex=\dfrac {2}{7}\\\\\largey=-5\ \dfrac {4}{7}$