Answer
When solving the given set of equations by the substitution method, we obtain\[10=10\], so the solution set is infinite. If you attempt to solve such a system by graphing, you will obtain two lines that are parallel (coincident).
Work Step by Step
Given equations are\[x=3y+2\ \text{and }5x-15y=10\]and, \[10=10\].
Substitute the value of \[x\]from first equation in the second equation as:
\[\begin{align}
& 5\left( 3y+2 \right)-15y=10 \\
& 15y+10-15y=10 \\
& 10=10
\end{align}\]
Thus, the system has infinite number of solutions.
The graph shown below of the equations show that the lines are parallel (same lines), i.e., they have an infinite number of solutions.
