Question

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

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

Short 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-by-step solution

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.