Find the value of $a$ for which the system of equations
\begin{align*}
y &= 11x+14 \\
2y-4 &= ax + y - 6
\end{align*}
has no solutions.
+129771 Substitute the first equation into the second equation for y
2 ( 11x + 14) - 4 = ax + (11x + 14) - 6 simplify
1 ( 11x + 14) - 4 = ax - 6
11x + 14 - 4 = ax - 6
11x + 10 = ax - 6
11x = ax - 16
16 = ax - 11x
16 = x ( a - 11)
16 / ( a - 11) = x
This will have no solution when a = 11 because it will make the denominator of 16 / ( a -11) = 0
