Question

Solve each system of equations. If the system has no solution, say that it is inconsistent.

$\left\{\begin{array}{l}x+y=8\\ x-y=4\end{array}\right.$

Short answer

The solution of the given system of equation is $x=6,y=2;(6,2)$.

Step-by-step solution

Step 1. Given information.

The given equations are:

$$\begin{gathered} x+y=8 \\ x-y=4 \end{gathered}$$

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

The second equation can be written as:

$x=4+y$

Substitute this in the first equation.

$\begin{array}{rcl}(4+y)+y& =& 8\\ 4+2y& =& 8\\ 2y& =& 8-4\\ y& =& \frac{4}{2}\\ y& =& 2\end{array}$

Step 3. Determine the value of another variable.

Substitute $y=2$in $x=4+y$.

$$\begin{gathered} x=4+\left(2\right) \\ x=6 \end{gathered}$$

The solution of the given system of equation is $x=6,y=2;(6,2)$.