Question

Write a system of equations whose solution is

$x=\frac{\left|\begin{array}{cc}-6& 5\\ 30& -2\end{array}\right|}{\left|\begin{array}{cc}3& 5\\ 4& -2\end{array}\right|}$$y=\frac{\left|\begin{array}{cc}3& -6\\ 4& 30\end{array}\right|}{\left|\begin{array}{cc}3& 5\\ 4& -2\end{array}\right|}$

Short answer

The required system of equations is,

$3x+5y=-6$

$4x-2y=30$

Step-by-step solution

Step 1- Determine the approach that can be used

Using the Cramer’s rule for the value of x that is$x=\frac{\left|\begin{array}{cc}e& b\\ f& d\end{array}\right|}{\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|}$and comparing it with the provided value of x can help.

– Form the system of equations by using the approach 

Use the obtained approach and determine the value of a, b, c, d, e and f.

The obtained values are $a=3$, $b=5$, $c=4$, $d=-2$, $e=-6$ and $f=30$.

Use the obtained values and form the equations in the form of $ax+by=e$ and $cx+dy=f$.

$3x+5y=-6$

$4x-2y=30$

Step 3- Make the conclusion

As the obtained system of equations is representing the values which are in provided system of equations which means that the obtained equations are the required equations.