Question

Use Cramer's rule to solve this system of equations: $x+y=4$ and $2x+y=3$

• A. $x=-1,y=2$
• B. $x=1,y=-2$
• C. $x=2,y=5$
• D. $x=-1,y=5$

Answer 1

The correct option is D $x=-1,y=5$

Given, $x+y=4,2x+y=3$

Using Cramers rule, find the determinant of the coefficient matrix,

$D=\left|\begin{array}{cc}1& 1\\ 2& 1\end{array}\right|=1\times 1-(2\times 1)$ $=1-2$ $=-1$

Secondly, find the determinant of $x$ coefficient matrix,

$D_x=\left|\begin{array}{cc}4& 1\\ 3& 1\end{array}\right|=4\times 1-(3\times 1)$ $=4-3=1$

Similarly, find the determinant of $y$ coefficient matrix,

$D_y=\left|\begin{array}{cc}1& 4\\ 2& 3\end{array}\right|=3\times 1-(2\times 4)$ $=3-8=-5$

Applying Cramer's rule,

$x=\frac{D_x}{D}$

$\therefore x=\frac{1}{-1}=-1$

$y=\frac{D_y}{D}$

$\therefore y=\frac{-5}{-1}=5$

Therefore, $x=-1,y=5$