Question

Solve the following system using Cramer’s Rule.

$3x+5y=-7$

$x+4y=-14$

Answer 1

$3x+5y=-7$ -------------(1)

$x+4y=-14$-------------(2)

$D=\left|\begin{array}{cc}3& 5\\ 1& 4\end{array}\right|$

$=\left(3\right)\times \left(4\right)-1\times \left(5\right)$
$=12-5$
$=7$

$D_x=\left|\begin{array}{cc}-7& 5\\ -14& 4\end{array}\right|$

$=(-7)\times \left(4\right)-(-14)\times \left(5\right)$
$=-28+70$
$=42$

Now,
$D_y=\left|\begin{array}{cc}3& -7\\ 1& -14\end{array}\right|$

$=\left(3\right)\times (-14)-\left(1\right)\times (-7)$
$=-42+7$
$=-35$

Again,

$x=\frac{\left(D_x\right)}{D}$ and $y=\frac{\left(D_y\right)}{D}$

So, $x=\frac{42}{7}=6$

and

$y=\frac{(-35)}{7}=-5$

Hence,

$x=6\text{and}y=-5$