Q. 407 - Intermediate Algebra

Question

In the following exercises, solve the following systems by graphing.

$\left\{\begin{array}{l}x-y=5\\ x+2y=-4\end{array}\right.$

Step-by-Step Solution

Answer

The solution of the system of the equation $\left\{\begin{array}{l}x-y=5\\ x+2y=-4\end{array}\right.$ is the point of intersection $(2,-3)$

Step 1. Given

The system of equation is $\left\{\begin{array}{l}x-y=5\\ x+2y=-4\end{array}\right.$

To find the solution of equation by graphing 

Step 2. Find slope and y - intercept of first equation

Write the equation in the form of 

$x-y=5$

      $y=x-5$ which is the slope-intercept form.

So, slope $m=1$ and

                 $b=-5$

Step 3. Find slope and y - intercept of the second equation

Write the equation in the form of $y=mx+b$

$x+2y=-4$

      $2y=-4-x$

        $y=\frac{-4-x}{2}$

which is the slope-intercept form.

So, slope $m=-\frac{1}{2}$ and

                 $b=-2$

Step 4. Graph the lines

Graph the equation $x-y=5$ and

                                $x+2y=-4$

And find the point of intersection.

The point of intersection is $(2,-3)$

Step 5. Check the solution

Substitute the point $(2,-3)$ in the equation,

     $x-y=5$

$2-(-3)=5$

            $5=5$ is true.

Substitute the point $(2,-3)$ in the equation,

      $x+2y=-4$

$2+2(-3)=-4$

         $2-6=-4$

           $-4=-4$ is true.