Question

Use the matrix tool to solve the system of equations. Choose the correct ordered pair.5x - 4y = 28 7x + 5y = 18
A.(4, -2)
B.(3, -1)
C.(-2, 4)
D.(-1, 3)

Answer 1

$\left\{\begin{array}{ccc}5x-4y=28\\7x+5y=18\end{array}\right\\\begin{array}{ccc}(i)\\(ii)\end{array}\left[\begin{array}{ccc}5&-4\\7&5\end{array}\right\left|\begin{array}{ccc}28\\18\end{array}\right]\xrightarrow{(i):5}\left[\begin{array}{ccc}1&-\frac{4}{5}\\7&5\end{array}\right\left|\begin{array}{ccc}\frac{28}{5}\\18\end{array}\right]\xrightarrow{(ii)-7(i)}$
$\left[\begin{array}{ccc}1&-\frac{4}{5}\\0&\frac{53}{5}\end{array}\right\left|\begin{array}{ccc}\frac{28}{5}\\-\frac{106}{5}\end{array}\right]\xrightarrow{(ii)\cdot\frac{5}{53}}\\\left[\begin{array}{ccc}1&-\frac{4}{5}\\0&1\end{array}\right\left|\begin{array}{ccc}\frac{28}{5}\\-2\end{array}\right]\xrightarrow{(i)+(ii)\cdot\frac{4}{5}}$
$\left[\begin{array}{ccc}1&0\\0&1\end{array}\right\left|\begin{array}{ccc}4\\-2\end{array}\right]\\\\Answer:\boxed{ \left \{ {{x=4} \atop {y=-2}} \right. \to\fbox{A.}}$