Question

Solve the following simultaneous equations by using Cramer's rule: $3x-2y=3;2x+y=16$.

Answer 1

Given equations are $3x-2y=3$ and $2x+y=16$

The coefficient matrix is $A=\left[\begin{array}{cc}3& -2\\ 2& 1\end{array}\right]$

So we can write the given equations in matrix form as $\left[\begin{array}{cc}3& -2\\ 2& 1\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}3\\ 16\end{array}\right]$

Let $A_x$ be $\left[\begin{array}{cc}3& -2\\ 16& 1\end{array}\right]$ and $A_y$ be $\left[\begin{array}{cc}3& 3\\ 2& 16\end{array}\right]$

We get $|A|=7$ , $|A_x|=35$ and $|A_y|=42$

By cramers rule , we get $x=\frac{|A_x|}{|A|}=\frac{35}{7}=5$ and $y=\frac{|A_y|}{|A|}=\frac{42}{7}=6$