Question

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

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

Short 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-by-step solution

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.