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&-(4)/(5)\\7&5\end{array}\right\left|\begin{array}{ccc}(28)/(5)\\18\end{array}\right]\xrightarrow{(ii)-7(i)}`

`\left[\begin{array}{ccc}1&-(4)/(5)\\0&(53)/(5)\end{array}\right\left|\begin{array}{ccc}(28)/(5)\\-(106)/(5)\end{array}\right]\xrightarrow{(ii)\cdot(5)/(53)}\\\left[\begin{array}{ccc}1&-(4)/(5)\\0&1\end{array}\right\left|\begin{array}{ccc}(28)/(5)\\-2\end{array}\right]\xrightarrow{(i)+(ii)\cdot(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.}}`