Question

Use the matrix tool to solve the system of equations. Choose the correct ordered pair.4x + 5y = 13 8x - 2y = 14
A.(6, 3)
B.(3, 6)
C.(3, 4)
D.(2, 1)

Answer 1

$\left\{\begin{array}{ccc}4x+5y=13\\8x-2y=14\end{array}\right\\\begin{array}{ccc}(i)\\(ii)\end{array}\left[\begin{array}{ccc}4&5\\8&-2\end{array}\right\left|\begin{array}{ccc}13\\14\end{array}\right]\xrightarrow{(i):4}\left[\begin{array}{ccc}1&\frac{5}{4}\\8&-2\end{array}\right\left|\begin{array}{ccc}\frac{13}{4}\\14\end{array}\right]\xrightarrow{(ii)-8(i)}$
$\left[\begin{array}{ccc}1&\frac{5}{4}\\0&-12\end{array}\right\left|\begin{array}{ccc}\frac{13}{4}\\-12\end{array}\right]\xrightarrow{(ii):(-12)}\\\left[\begin{array}{ccc}1&\frac{5}{4}\\0&1\end{array}\right\left|\begin{array}{ccc}\frac{13}{4}\\1\end{array}\right]\xrightarrow{(i)-(ii)\cdot\frac{5}{4}}$
$\left[\begin{array}{ccc}1&0\\0&1\end{array}\right\left|\begin{array}{ccc}2\\1\end{array}\right]\\\\Answer:\boxed{ \left \{ {{x=2} \atop {y=1}} \right. \to\fbox{D.}}$