Question

Find the values of $x$ and $y$ for the system of equations, $x+y=2$ and $3x-y=6$ using Cramer's Rule.

• A. A unique solution
• B. No solutions
• C. An infinite number of solutions
• D. Zero solution as the only solution

Answer 1

The correct option is B No solutions

Given system of equation can be written as $\left[\begin{array}{cc}1& 1\\ 3& -1\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}2\\ 6\end{array}\right]$

$D=\left[\begin{array}{cc}1& 1\\ 3& -1\end{array}\right]=-4$

$D_1=\left[\begin{array}{cc}2& 1\\ 6& -1\end{array}\right]=-8$

$D_2=\left[\begin{array}{cc}1& 2\\ 3& 6\end{array}\right]=0$
$\Rightarrow x=\frac{D_1}{D}=\frac{-8}{-4}=2$ and

$y=\frac{D_2}{D}=\frac{0}{-4}=0$