Chapter 6.1, Problem 9P

Solve each system by graphing. Check your solution.

$y=-\frac{2}{5}x-2$

$y=-x-5$

To determine

To Graph and Check: The system of equations by graphing method and check.

Answer to Problem 9P

Solution is (-5,0); $x=-5$ and $y=0$

Explanation of Solution

Given information: The given equations are $y=-\frac{2}{5}x-2$ ------(1)

And $y=-x-5$ -----(2)

Graph:

Use slope and y intercept method to graph the lines.

For equation (1)

  $y=-\frac{2}{5}x-2$

Slope $=-\frac{2}{5}$ and y intercept $=-2$

Represent the y intercept (0,-2). Using slope find the another point.

Slope $=\frac{Rise}{Run}=\frac{-2}{5}$

Rise =-2

Run =5

So, from y intercept move down 2 units(because rise is -2) and right 5 units(because run is 5) to get another point. Then join the points and extend the line on both ends.

For equation (2)

Slope $=-1$ and y intercept $=-5$

Slope $=\frac{Rise}{Run}=\frac{-1}{1}$

Rise =-1

Run =1

So, represent the y intercept (0,-5) on xy plane. Using slope find another point. From y intercept move down 1 unit(because rise is -1) and right 1 unit(because run is 1) to get another point. Then join the points and extend the line.

The graph of the lines are

  

Interpretation: The Purple line represents equation (1) and Green line represents equation (2). Solution set is where the lines intersect. The solution set is (-5,0).

Check:

Plug in x as -5 and y as 0 into the equations then simplify to see whether the equations are true or not.

For equation (1)

  $0=-\frac{2}{5}(-5)-2$

Simplify the right side of the equation

  $0=2-2$

  $0=0$

Yes! The equation is true for the solution (-5,1) so, it is solution to the equation.

For equation (2)

  $0=-(-5)-5$

  $0=5-5$

  $0=0$

Yes! The equation is true for (-5,0) so, this is solution to the equation.

Both equations are true for the solution set.

Hence the (-5,0) is the solution to the system of equations.