Question

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$\left\{\begin{array}{r}x+2y=-7\\ x+y=-3\end{array}\right.$

Short answer

The solution of the given system of equation is $x=1,y=-4;(1,-4)$.

Step-by-step solution

Step 1. Given information.

The given equations are:

$\begin{array}{rcl}x+2y& =& -7\\ x+y& =& -3\end{array}$

Step 2. Determine the value of one variable by substitution.

The second equation can be written as:

$x=-3-y$

Substitute this in the first equation.

$\begin{array}{rcl}(-3-y)+2y& =& -7\\ -3+y& =& -7\\ y& =& -7+3\\ y& =& -4\end{array}$

Step 3. Determine the value of another variable.

Substitute $y=-4$in $x=-3-y$.

$\begin{array}{rcl}x& =& -3-(-4)\\ & =& -3+4\\ & =& 1\end{array}$

The solution of the given system of equation is $x=1,y=-4;(1,-4)$.