Answer
The table length without leaves is 4 feet.
Work Step by Step
The first step is to write and define the variables in use. In this case, we can use x for the table without leaves and y for the length of a single leaf.
We can then write the equations out using the information given in the problem. This would come to $x+y = 5.5$ and $x+2y=7$.
In order to solve this system, we can use elimination. In order to do this, we must first multiply $x+y = 5.5$ by -1; this will allow for the coefficients in the second equation to match. Since we now have the same X coefficient with opposing signs ($-x-y = -5.5$ and $x+2y=7$) , we can add the equations together:
$-x-y = -5.5$ +
$x+2y=7$
This addition will eliminate the x variable. The $2y$ will add to the $-y$ to yield a single $y$, and $-5.5 + 7 $ will give a return of $1.5$, meaning that $y=1.5$.
We can then substitute $y=1.5$ into any equation from above. For this example, we substituted back into $x+y=5.5$. This comes to $ x+ (-1.5) = 5.5$.
Solving for this equation gives us 4, which means that the table length without leaves is 4 feet in length.
