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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.

 Aug 14, 2023
 #1
avatar+128732 
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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

 

cool cool cool

 Aug 14, 2023

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