Question

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

$\left\{\begin{array}{l}-4x+y=0\\ 6x-2y=14\end{array}\right.$

Short answer

The solution for the system of equations$\left\{\begin{array}{l}-4x+y=0\\ 6x-2y=14\end{array}\right.$is,$x=-7,y=-28$.

Step-by-step solution

Step 1. Given information

$\left\{\begin{array}{l}-4x+y=0\\ 6x-2y=14\end{array}\right.$

The inverse found in problem$34$is,$\left[\begin{array}{cc}-1& \frac{-1}{2}\\ -3& -2\end{array}\right]$.

Step 2. We know that, X=A-1.B

From the given information, $B=\left[\begin{array}{c}0\\ 14\end{array}\right]$.

Substitute the known values in the formula.

$$\begin{gathered} \left[\begin{array}{c}x\\ y\end{array}\right]=X \\ X=\left[\begin{array}{cc}-1& \frac{-1}{2}\\ -3& -2\end{array}\right]\left[\begin{array}{c}0\\ 14\end{array}\right] \\ =\left[\begin{array}{c}-1\left(0\right)-\frac{1}{2}\left(14\right)\\ -3\left(0\right)-2\left(14\right)\end{array}\right] \\ =\left[\begin{array}{c}0-7\\ 0-28\end{array}\right] \\ =\left[\begin{array}{c}-7\\ -28\end{array}\right] \end{gathered}$$

So, the solution is, in ordered pairs$\left(-7,-28\right)$or$x=-7,y=-28$.