Solve the given system of linear equations. Enter your answer as a point (or ordered pair of numbers) in the form of \( ( x , y ) \) . \( 3 x - 5 y = 27 \) \( 5 x - 3 y = 13\) 

Solve using the Cramer's rule

\(\left ( x,y\right ) = \left ( - 1,- 6\right ) \)

SOLUTION

Solve the equation

\(\left \{ \begin{array} { l} x= \frac { 27+ 5y} { 3} \\ 5x- 3y= 13\end{array} \right .\)   

Solve using substitution

\(5\times \frac { 27+ 5y} { 3} - 3y= 13\)   

Simplify

\(\frac { 135+ 16y} { 3} = 13\)   

Cross multiply

\(135+ 16y= 3\times 13\)   

Evaluate

\(135+ 16y= 39\)   

Move the constant to the right side

\(16y= 39- 135\)   

Subtract the terms

\(16y= - 96\)   

Divide both sides

\(\frac { 16y} { 16} = \frac { - 96} { 16} \)   

Simplify

\(\frac { 16y} { 16} = - 6\)   

Simplify

\(y= - 6\)  \(\text { Substitute the value of } y\)  \(x= \frac { 27+ 5\left ( - 6\right ) } { 3} \)   

Simplify

\(x= - 1\)   

Calculate

\(\left \{ \begin{array} { l} x= - 1\\ y= - 6\end{array} \right .\)   

Check the solution

\(\left \{ \begin{array} { l} x= - 1\\ y= - 6\end{array} \right .\)