Q. 410 - Intermediate Algebra

Question

In the following exercises, solve each system of equations. Use either substitution or elimination.

$\left\{\begin{array}{l}-3x+4y=25\\ x-5y=-23\end{array}\right.$

Step-by-Step Solution

Answer

The solution to the system of equations $\left\{\begin{array}{l}-3x+4y=25\\ x-5y=-23\end{array}\right.$ is $(-3,4)$

Step 1. Given

The system of equations $\left\{\begin{array}{l}-3x+4y=25\\ x-5y=-23\end{array}\right.$

To find the solution of the system of equations.

Step 2. Solve the equations

Consider the system of equations: 

$-3x+4y=25$

     $x-5y=-23$

Solve the second equation for $x$,

              $x=-23+5y$

Step 3. Solve for y

Substitute $x=-23+5y$ in the first equation,

                 $-3x+4y=25$

$-3(-23+5y)+4y=25$

         $69-15y+4y=25$

                     $-11y=25-69$

                     $-11y=-44$

Divide both sides of the equation by $-11$,

                             $y=4$

Step 4. Solve for x

Substitute $y=4$ in the second equation,

   $x-5y=-23$

$x-5\left(4\right)=-23$

          $x=-23+20$

          $x=-3$

The solution of the system of equation is $(-3,4)$

Step 5. Check the solution

Substitute $(-3,4)$ in both the equations,

        $-3x+4y=25$

$-3(-3)+4\left(4\right)=25$

             $9+16=25$

                   $25=25$ is true.

Then, $x-5y=-23$

$(-3)-5\left(4\right)=-23$

            $-23=-23$ is true.

Hence the solution has been checked.