Chapter 11.1, Problem 18AYU

To determine

To find:The solution of the given system of equations.

Answer to Problem 18AYU

Solution:

  $x=1,y=-4$

Explanation of Solution

Given:

  $x+2y=-7$

  $x+y=-3$

Calculation:

The system of equations is,

  $x+2y=-7$

  $x+y=-3$

Subtracting these two equations we get,

  $(x+2y)-(x+y)=-7-(-3)$

  $x+2y-x-y=-7+3$

  $y=-4$

Substituting $y=-4$ in the second equation we get,

  $x+(-4)=-3$

  $x-4=-3$

  $x=-3+4$

  $x=1$

Thus $x=1,y=-4$ is the solution of the given system of equations.

The graph is as follows:

  

From the graph we see that (1,-4) is the point of intersection of these two given lines: $x+2y=-7$ and $x+y=-3$ .