Answer
When solving the given set of equations by addition method, we obtain \[0=3\], so the solution set is empty. If you attempt to solve such a system by graphing, you will obtain two lines that are non-intersecting.
Work Step by Step
Given equations are:\[12x-21y=24\ \text{and }4x-7y=7\]and, \[0=3\].
To eliminate\[x\], second equation is multiplied by\[-3\].Thus,
\[\begin{align}
& \left( 4x-7y=7 \right)\times -3 \\
& -12x+21y=-21 \\
\end{align}\]
Now, add the above new equation to the first equation to eliminate\[x\]as:
\[\begin{align}
& \left( -12x+21y \right)+\left( 12x-21y \right)=-21+24 \\
& 0=3
\end{align}\]
which is not possible, thus the solution set is empty.
The graph of the equations show that the lines are non-intersecting, i.e., they don’t have a common solution.
