Question

In Problems $41-60$, use the inverses found in Problems $31-40$to solve each system of equations.

role="math" localid="1647420018361" $\left\{\begin{array}{l}3x-y=8\\ -2x+y=4\end{array}\right.$

Short answer

The solution for the system of equations$\left\{\begin{array}{l}3x-y=8\\ -2x+y=4\end{array}\right.$is,$x=12,y=28$.

Step-by-step solution

Step 1. Given information

$\left\{\begin{array}{l}3x-y=8\\ -2x+y=4\end{array}\right.$

The inverse found in problem $32$is, $\left[\begin{array}{cc}1& 1\\ 2& 3\end{array}\right]$.

Step 2. We know that, X=A-1.B

From the given information, $B=\left[\begin{array}{c}8\\ 4\end{array}\right]$.

Substitute the known values in the formula.

role="math" localid="1647420384652" $$\begin{gathered} \left[\begin{array}{c}x\\ y\end{array}\right]=X \\ X=\left[\begin{array}{cc}1& 1\\ 2& 3\end{array}\right]\left[\begin{array}{c}8\\ 4\end{array}\right] \\ =\left[\begin{array}{c}\left(1\times 8\right)+1\left(4\right)\\ \left(2\times 8\right)+3\left(4\right)\end{array}\right] \\ =\left[\begin{array}{c}8+4\\ 16+12\end{array}\right] \\ =\left[\begin{array}{c}12\\ 28\end{array}\right] \end{gathered}$$

So, the solution is, in ordered pairs $\left(12,28\right)$or $x=12,y=28$.