Question

Use the matrix tool to solve the system of equations. Choose the correct ordered pair.3x - 8y = -1 -2x + 6y = 1 A.(1, 1/2) B.(1/2, 3) C.(1/2, 1) D.(3,1/2)

Answer 1

$\left\{\begin{array}{ccc}3x-8y=-1\\-2x+6y=1\end{array}\right\\\begin{array}{ccc}(i)\\(ii)\end{array}\left[\begin{array}{ccc}3&-8\\-2&6\end{array}\right\left|\begin{array}{ccc}-1\\1\end{array}\right]\xrightarrow{(i):3}\left[\begin{array}{ccc}1&-\frac{8}{3}\\-2&6\end{array}\right\left|\begin{array}{ccc}-\frac{1}{3}\\1\end{array}\right]\xrightarrow{(ii)+2(i)}$
$\left[\begin{array}{ccc}1&-\frac{8}{3}\\0&\frac{2}{3}\end{array}\right\left|\begin{array}{ccc}-\frac{1}{3}\\\frac{1}{3}\end{array}\right]\xrightarrow{(ii)\cdot\frac{3}{2}}\\\left[\begin{array}{ccc}1&-\frac{8}{3}\\0&1\end{array}\right\left|\begin{array}{ccc}-\frac{1}{3}\\\frac{1}{2}\end{array}\right]\xrightarrow{(i)+(ii)\cdot\frac{8}{3}}\\\left[\begin{array}{ccc}1&0\\0&1\end{array}\right\left|\begin{array}{ccc}1\\\frac{1}{2}\end{array}\right]$

$Answer:\boxed{ \left \{ {{x=1} \atop {y=\frac{1}{2}}} \right.\to\fbox{A.}}$