Chapter 11.3, Problem 21AYU

In Problem 15-42, solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, write, “Not applicable”.

$\{\begin{array}{c}4x-6y=-42\\ 7x+4y=-1\end{array}$

To determine

The solution of the system of linear equations using Cramer’s rule,

$\{\begin{array}{l}4x-6y=-42\\ 7x+4y=-1\end{array}$

Answer to Problem 21AYU

Solution:

The solution of the system $\{\begin{array}{l}4x-6y=-42\\ 7x+4y=-1\end{array}$ is $x=-3,\text{}\text{}y=5$ or $\left(-3,5\right)$.

Explanation of Solution

Given information:

The system of linear equations, $\{\begin{array}{l}4x-6y=-42\\ 7x+4y=-1\end{array}$

Explanation:

To solve this system using Cramer’s Rule, first find the value of determinant D of the coefficient of the variable.

Therefore, determinant becomes

$\left|\begin{array}{cc}4& -6\\ 7& 4\end{array}\right|=(4)(4)-(7)(-6)=16+42=58$.

Here $D\ne 0$, then we can find the values of $D_x,\text{}\text{}{D}_y$.

To find $D_x$ replace the coefficient of $x$ in $D$ with the constant and then evaluate the determinant.

$D_x=\left|\begin{array}{cc}-42& -6\\ -1& 4\end{array}\right|=(-42)(4)-(-6)(-1)=-168-6=-174$

And $D_y=\left|\begin{array}{cc}4& -42\\ 7& -1\end{array}\right|=(4)(-1)-(-42)(7)=-4+294=290$

So the values of $x,y$ as,

$x=\frac{D_x}{D}=\frac{-174}{58}=-3$ and $y=\frac{D_y}{D}=\frac{290}{58}=5$.

The solution of system of equations using Cramer’s Rule is $x=-3,y=5$ or using ordered pair $\left(-3,5\right)$.