Question

Using Cramer's rule, solve for the values of x and y.

$3x+5y=29$

$7x+3y=33$

• A. $x=-4,y=-3$
• B. $x=4,y=3$
• C. $x=3,y=4$
• D. $x=-3,y=-4$

Answer 1

The correct option is C $x=3,y=4$

$3x+5y=29$ -------------(1)

$7x+3y=33$-------------(2)

According to Cramer's Rule , we have,

$D=\left|\begin{array}{cc}3& 5\\ 7& 3\end{array}\right|=3\times 3-5\times 7$
$=9-35$
$=-26$

$D_x=\left|\begin{array}{cc}29& 5\\ 33& 3\end{array}\right|=29\times 3-5\times 33$
$=87-165$
$=-78$

$D_y=\left|\begin{array}{cc}3& 29\\ 7& 33\end{array}\right|=3\times 33-7\times 29$
$=99-203$
$=-104$

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

So,
$x=\frac{(-78)}{-26}=3$

and

$y=\frac{(-104)}{-26}=4$