Question

Use the matrix tool to solve the system of equations. Choose the correct ordered pair.7x - 4y = 13 2x - 5y = -4

Answer 1

Solutions 

In Matrix we use initially based on systems of linear equations.The matrix method is similar to the method of Elimination as but is a lot cleaner than the elimination method.Solving systems of equations by Matrix Method involves expressing the system of equations in form of a matrix and then reducing that matrix into what is known as Row Echelon Form. 

Calculations 

⇒ Rewrite the linear equations above as a matrix 

$\left[\begin{array}{ccc}7&-4&13\\2&-5&-4\\\end{array}\right]$ 

⇒  Apply to Row₂ : Row₂ - 2/7 Row₁ 

$\left[\begin{array}{ccc}7&-4&13\\0&-27/7&-54/7\\\end{array}\right]$ 

⇒ Simplify rows 

$\left[\begin{array}{ccc}7&-4&13\\0&1&2\\\end{array}\right]$ 

Note: The matrix is now in echelon form.
The steps below are for back substitution. 

⇒ Apply to Row₁ : Row₁ + 4 Row₂ 

$\left[\begin{array}{ccc}7&0&21\\0&1&2\\\end{array}\right]$

⇒ Simplify rows 

$\left[\begin{array}{ccc}1&0&3\\0&1&2\\\end{array}\right]$ 

⇒ Therefore, 

$x=3 y=2$

Answer 2

$\left\{\begin{array}{ccc}7x-4y=13\\2x-5y=-4\end{array}\right\\\begin{array}{ccc}(i)\\(ii)\end{array}\left[\begin{array}{ccc}7&-4\\2&-5\end{array}\right\left|\begin{array}{ccc}13\\-4\end{array}\right]\xrightarrow{(i):7}\left[\begin{array}{ccc}1&-\frac{4}{7}\\2&-5\end{array}\right\left|\begin{array}{ccc}\frac{13}{7}\\-4\end{array}\right]\xrightarrow{(ii)-2(i)}$
$\left[\begin{array}{ccc}1&-\frac{4}{7}\\0&-\frac{27}{7}\end{array}\right\left|\begin{array}{ccc}\frac{13}{7}\\-\frac{54}{7}\end{array}\right]\xrightarrow{(ii)\cdot(-\frac{7}{27})}\\\\\left[\begin{array}{ccc}1&-\frac{4}{7}\\0&1\end{array}\right\left|\begin{array}{ccc}\frac{13}{7}\\2\end{array}\right]\xrightarrow{(i)+(ii)\cdot\frac{4}{7}}$
$\left[\begin{array}{ccc}1&0\\0&1\end{array}\right\left|\begin{array}{ccc}3\\2\end{array}\right]\\\\Answer:\boxed{ \left \{ {{x=3} \atop {y=2}} \right. }\to\fbox{B.}$