Question

Solve the following system using Cramer’s Rule.

$3x+5y=-7$

$x+4y=-14$

• A. $x=-6\text{and}y=-5$
• B. $x=6\text{and}y=-5$
• C. $x=5\text{and}y=-6$
• D. $x=-6\text{and}y=5$

Answer 1

The correct option is B $x=6\text{and}y=-5$

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

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

$D=\left|\begin{array}{cc}3& 5\\ 1& 4\end{array}\right|=3\times 4-5\times 1$
$=12-5$
$=7$

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

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

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

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

Again,

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

So, $x=\frac{\left(42\right)}{7}=6$ and $y=\frac{(-35)}{7}=-5$

Hence,

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