Answer
Makes sense
Work Step by Step
Take point any fractions as solution in the graph and determine if the set is reasonable. After all fractions are real numbers and any real number can be represented on the Cartesian system.
For example, consider a system,
\[\left\{ \begin{align}
& 3x+2y=7 \\
& x+2y=2 \\
\end{align} \right.\]
There are two linear equations. Subtract one equation from the other.
\[\begin{align}
& \left( 3x+2y \right)-\left( x+2y \right)=7-2 \\
& 3x+2y-x-2y=5 \\
& 2x=5 \\
& x=\frac{5}{2}
\end{align}\]
Now put the value of x in first equation.
\[\begin{align}
& 3x+2y=7 \\
& 3\left( \frac{5}{2} \right)+2y=7 \\
& 2y=7-\frac{15}{2} \\
& y=\frac{14-15}{4}
\end{align}\]
Further solve,
\[y=-\frac{1}{4}\]
So, the above system of linear equation has unique solution, that is, \[\left\{ \frac{5}{2},-\frac{1}{4} \right\}\]. Solution can be represented on plane for \[x=2.5\]and\[y=-0.25\].
Hence, a linear system involving fractions as a solution set can be used in graphs to determine if the solution set is reasonable.
